List of Numberblock Clubs/Fanmade

This club is for numbers who can make a thin escalator shape (bottom layer = 4 | no-end layers = 4 | top layer = 3).

Members include: 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 95, 99, etc.

The formula is $4n+3$ .

"F" Shape Club[]

This club is for numbers that have four same straight lines with two points together.

Members include: 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97, etc.

The formula is $4n+5$ .

High Five Club[]

(by Eating Crocodiles All The Time)

Numbers multiplied by 5 (or 10 given the fact 2x5 = 10) can join this club. It is related to Made Of Ones Club, Even Tops and Three Club.

The formula is $5n$ .

The badge will have a picture of Five's glove on it with the number 5 on it and even compound Numberblocks multiplied by 5 can join. The members are Five, Ten, Fifteen, Twenty, Twenty-Five, Thirty, Thirty-Five, Forty, Forty-Five, Fifty, Fifty-Five, Sixty, Seventy, Eighty, Ninety and One Hundred, in an episode called "Too Many Threes", it is shown that Three is the founder of Three Club, so Five must be the founder of High Five Club.

"L" Shape Club[]

(by G3498)

This club is for numbers has 3 straight lines with 1 point together.

members include: 4, 6, 8, 10, 12, 14, 16, 18, 20, etc.

The formula is $3n+1$

Ladder Club[]

(by Eating Crocodiles All The Time)

Ladder Club is for numbers who can make a ladder shape. It's a bit similar to Tower With Windows Club, but with 2 blocks removed from top to bottom.

The formula is $5n+2$ .

Members are: 7, 12, 17, 22, 27, 32. Numberblocks five more than seven or the number before can join this club.

Tower With Windows Club[]

The "Tower With Windows" Club is based off of the shape with the same name in the episode Making Patterns, which can make rectangles that are three blocks wide, an odd number of blocks tall, and missing the middle block of each even numbered row. Members of this club also consequently always end in 3 or 8, but 3 is not a member of this club. Members of this club include 8, 13, 18, 23 and 28.

The formula is $5n+3$ .

Hourglass Club[]

Hourglass Club is for numbers who can make an hourglass shape, but a block is between the holes if it's more than 10 which looks like the water level.

Members include: 9, 14, 19, 24, 29, 34, 39, 44, 49, 54, 59, 64, 69, 74, 79, 84, 89, 94, 99, etc.

The formula is $5n+4$ .

"P" Shape Club[]

This club is for numbers that have a square with a hole stick to 1 by any blocks which's almost less blocks wide than a square with a hole's blocks wide. (Four does not have square with a hole.)

Members include: 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, etc.

The formula is $5n+5$ .

Note: This club only features multiples of 5.

"E" Shape Club[]

This club is for numbers that have five same straight lines with three points together.

Members include: 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, 76, 81, 86, 91, 96, etc.

The formula is $5n+6$ .

Octahedron Club[]

The Octahedron Club is for numbers who can make a octahedron shape; or put simply, making a 3D shape where six one-block wide rods of equal length extend from a single block. All members of this club are odd, and it is also the 3D equivalent of Cross Club. Members of this club include 7, 13, 19, 25, 31 and 37.

The formula is $6n+1$ .

Zero is Here-O![]

(by JaysonP65132) This club vanishes things and appear out of nowhere. They even have a Times Table, just not real... They're really impressive. This club includes multiples of 0. Fine, I admit it-0 is the only member.

The formula is $0n$

Fours on the Floor[]

(by JaysonP65132) This groovy dancing club include multiples of 4.

Friendly Fours[]

By Maddox Crabb (alt account).

The Friendly Fours Club, like the Fours on the Floor club, is made for multiples of Four. This club's formula is $4n$ .

Fun with Fours[]

By Alexlaugher2

The Fun with Fours Club, like the Fours on the Floor club and the Friendly Fours club, is made for multiples of 4.

Five Jivers[]

(by JaysonP65132) This club is a professional band inspired by All Star Line Up. All the members are multiples of 5.

Six Remixers[]

(by JaysonP65132) This is a playful DJ group that also likes playing board games. This group was inspired by the episode "Remix the Sixes". All the members are multiples of 6. $6n$ is the formula.

Heroic Eights Club[]

(by GreatControl76) This club is for multiples of 8.

Members include: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, etc.

The formula is $8n$ . It's named because Eight becomes Octoblock and Eighty becomes Super Octoblock, they're heroes.

Sneeze Club[]

By XhanLu, referred to as "Achooo Club" by Forty Eight, Activate.

This club is for multiples of 9.

Members include: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, etc.

The formula is $9n$ . It's named because Nine sneezes-'scuse me...ah..ah...ACHOOO!!!!!

Magical Nines[]

(by JaysonP65132) Like the Sneeze Club, this club is about multiples of nine. Unlike Sneeze Club, this club has a theme on magic. It is inspired by Ninety.

Heroes With Zeroes[]

(by FIVE GLOVE SLAPPIN)

"Heroes With Zeroes" Club is obviously similar to the Numberblocks episode, Heroes With Zeroes, Numberblocks divisible by 10 can join this, as you may have known.

Everybody knows the members: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100. Ten is the owner, and it’s similar to the Made-Of-Ones Club, but you just need an extra zero to make your favourite heroes in the club. There is a badge with red sides and a white base with a rocket with the number 10 on it.

The formula is $10n$ .

Twelves in Zen[]

(by JaysonP65132) This is a calm and peaceful club that meditate to train their super-ray powers. All the members are multiples of 12: Twelve, Twenty-Four, Thirty-Six, Forty-Eight, Sixty, Seventy-Two, Eighty-Four, Ninety-Six, One Hundred Eight, One Hundred Twenty, One Hundred Thirty-Two, and One Hundred Forty-Four.

Calendar Club[]

(by Mdos5)

This club is for multiples of 31. Its members are 31, 62, 93, and 310. The founder and most active member of the club is 310, who loves calendars SO much and wears his badge all the time!

Mdos5CalenderClubBadge — The badge of Calendar Club.

Mdos5310 — 310, the founder and most active member of the club.

Double-Lover Club[]

(By Numberfuture98)

This club is only for multiples of Thirty-Two

Their members are 32, 64, 96, 128, 160 etc.

The formula is $32n$ .

2-Enders Club[]

This club is for numbers which is in formula $10n+2$ .

3-Enders Club[]

This club is for numbers which is in formula $10n+3$ .

4-Enders Club[]

(by GreatControl76) This club is for numbers which is in formula $10n+4$ .

5-Enders Club (also known as Odd Five Club)[]

This club is for numbers which is in formula $10n + 5$ .

6-Enders Club[]

This club is for numbers which is in formula $10n+6$ .

7-Enders Club[]

This club is for numbers which is in formula $10n+7$ .

8-Enders Club[]

This club is for numbers which is in formula $10n+8$ .

20 Roaring Club[]

This club is for Numbers that are between 2000 and 2099.

Members include 2000, 2001, 2002, 2003 ect.

Wireframe Club[]

The "Wireframe" Club is for numbers that can only form the borders of a cube, and not the rest. Members of this club include 20, 32, and 44, with 44 being the leader of this club.

The formula is $12n+8$ .

Four-Holed Squares Club[]

(by XhanLu, concept by MrQwerty12309)

Club for numbers that can make a square with only the frame and the middle rows, forming a window shape. Members include: 21, 33, 45, 57, 69 and 81.

The formula is $(2n+3)^2-4n^2$ , or $12n+9$ .

Square Party Club[]

This club is for multiples of 16 (16, 32, 48, 64, 80, etc). This club gets its name from one of 16’s phrases.

The formula is $16n$ .

The Artistic 17s club[]

(By Punchcar63)

This club is for multiples of 17. Members include 17, 34, 51, 68 and so on.

The formula is $17n$ .

Crazy Shapes Club[]

(by JustArandomSquare)

This club is for multiples of 19, The members of this club are 19, 38, 57, 76 and 95.

The formula is $19n$ .

Cicada Club[]

Jz cicada — 12, 32, 52, 72, 92 in Cicada Club

(by JingzheChina and Plain)

This club is for numberblocks with a Twelve as head and Twenties as body. A typical "cicada" is Thirty-Two, where her Twelve-head like the cicada head, and the other ten-blocks look like the wings, and the whole of Thirty-Two looks like a cicada.

According to this logic, Twelve herself is "ci", Fifty-Two is "cicada-cada", Seventy-Two is "cicada-cada-cada" and so on.

The founder of this club is Ninety-Two, or "cicada-cada-cada-cada".

The formula is $20n+12$ .

22's Club[]

4CE07CEC-FBE5-4751-BC4D-290AE475B123 — The badge.

(By Kristan12)

This club is for multiples of Twenty-Two.

The formula is $22n$ .

29's Club[]

(By ThatGuy30722)

This club is for multiples of Twenty-Nine.

The formula is $29n$ .

43 Chars Club[]

(By Connorclarke107)

This club is for multiples of 43. This club gets its name from the "43 chars" meme.

Members include 43, 86, 129, 172, 215, etc.

The formula is $43n$

Sophie Piper Fan Club[]

(By Connorclarke107)

This club is for multiples of 44 (Connorclarke107's favorite number), because of the fact that Sophie Piper is the aforementioned user's favorite Halloweentown character. This is a sub-club of Even Tops, Square with a Hole Club, League of Elevens, and Super Rectangle Club.

Members of the Sophie Piper Fan Club include 44, 88, 132, 176, 220, etc.

The formula is $44n$ .

70n+6 Cute Friends Club[]

(by Asaki88bbff)

This club is for 70n+6 numbers. From 76 to 496 every member has their own different patterns (such as octahedron 146 and cube 216), but the n^th member can also make a squad of centered 2n-gons, or centered 2n-gonal pyramid. Their personalities are all cute and warm, and they are good friends.

Members include 76, 146, 216, 286, 356, 426, 496, ... 146 and 216 are sisters, and founded this club.

The formula is $70n+6$ .

Michelle Tanner Club[]

This club is for mutiples of 53. These Numberblocks are specialised Full House fans and would often refer to it as the Baby Michelle Show. They all have a role in the Michelle Tanner Hotel owned by 530.

Members include 53, 106, 159, 212, 265, etc.

The formula is $53n$

X-Box Club[]

This club is for Numberblocks with can arrange in the following pattern: a letter "X" on each face of a cube box, with three-diagonal width and without four corners.

The formula is $72n+6$ with $n \in \mathbb{N}^+$

A113 Club[]

This club is for multiples of 113. This club gets its name from A113, an easter egg seen in every Pixar film except Monsters Inc.

Members include 113, 226, 339, 452, 565, 678, etc.

The club's badge is a Pixar ball with the code A113 on it.

The formula is $113n$

185's Club[]

Jz185tt — JingzheChina's 185, 370, 555, 740, 925 with the 185 Times Table

This club is for multiples of 185. All the number corresponds to a song which expresses my feeling.

Members include 185, 370, 555, 740, 925, etc.

The formula is $185n$ .

The Speedy 18's Club[]

(by AamirGamingTvNew)

This club is for multiples of 18. The founder of the club is likely 18 or 180.

Members include 18, 36, 54, 72, 90, 108, etc.

The formula is $18n$ .

Quadratic function clubs[]

Quadratic function clubs can be written as $an^2+bn+c$ , where $a$ , $b$ , and $c$ are real constants.

Not Quite a Square Club[]

The Not quite a square club is for numbers who are one row of blocks off from being a square.

Members include 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132 etc.

The Formula is $n (n - 1)$ or $n^2-n$ .

Jellyfish Club[]

(by Asaki88bbff)

The Jellyfish Club is for numbers that can make a jellyfish shape (heptagonal numbers).

Members include 1,7,18,34,55,81...

The formula is $n(5n-3) \over 2$ or $5n^{2}-3n \over 2$ .

Boat Club[]

(By Asaki88bbff)

This club is for numbers that can make a boat shape (octagonal numbers).

Members: 1, 8, 21, 40, 65, 96, etc.

The formula is $3n^2-2n$ .

Long Jellyfish Club[]

(by Asaki88bbff)

The Long Jellyfish Club is for numbers that can make a long jellyfish shape(nonagonal numbers).

Members include 1,9,24,46,75...

The formula is $n(7n-5) \over 2$ or $7n^{2}-5n \over 2$ .

House Club[]

(By XhanLu)

The House club is for numbers that can make a house shape.

Members include 3, 12, 27, 48, 75 etc.

The formula is $n^2-{n \over 4}$ ,where $n$ is even.

2D Lemon Club[]

This club is for numberblocks which can make a 2D lemon shape (a non-standard hexagon shape).

The formula is $4x^{2}-5x+2$ .

Rectangular Spiral Club[]

(by Lookiecookie0505,and Asaki88bbff has same idea)

The "Rectangular Spiral" Club is for numbers who can form a spiral, which starts by selecting a rectangle of dimensions x by x+1, and then coiling blocks in loops to fill the maximum amount of space without self-intersections. Members of this club include 5, 9, 14, 20, and 27.

The formula is $0.5x^2+2.5x+2$ .

Double Rectangular Spiral Club[]

(by Asaki88bbff)

The Double Rectangular Spiral Club is for numbers that can make a double rectangular spiral shape.They are also squares -2.

Members include 2, 7, 14, 23, 34, 47, ...

The formula is $n^2-2$ .

Square Spiral club[]

(by Asaki88bbff)

The Square Spiral Club is for numbers that can make a square spiral shape. And they can also make a pattern that made of 4 rectangular spirals. They are all two less than centered squares.

Members include 3, 11, 23, 39, 59, 83, ..., and the formula is $2n^2+2n-1$ .

Right Triangle Club[]

The "Right Triangle" club are for Numberblocks that can create a right triangle; similar to a Step Squad, but it's more of a ramp rather than a staircase. The owner of this club is 4.5.

Members include 0.5, 2, 4.5, 8, 12.5, 18, 24.5 etc.

The formula is $\frac{n^2}{2}$ .

Hollow Cube Club[]

(by Mr. Yokai)

The "Hollow Cube" Club, is a club which consists of a cube that doesn't have any inner blocks when they make a club. The owner of this club is 56. The formula is $n^3-(n-2)^3$ or $n^2-4n+8$ , where $n>2$ , so 26, 56, and 98 are a part of it.

Chippy Square Club[]

If you're able to make an chippy square, you can join this club. Two can't join since he can only make a diamond. Members of this club include Seven, Fourteen, Twenty-Three, Thirty-Four, and Forty-Seven (being the owner).

The formula is $n^2-2$ , where $n>2$ .

One Off a Square Club[]

(by TSRITW)

The "One Off a Square" Club is for numbers that are one less than a square number. Members on this club include 3, 8, 15, and 24.

The formula is $(n-1)(n+1)$ or $n^2 - 1$ .

Square Stamp Club[]

This club is for numbers who can arrange in a furry square, like a stamp.

The formula is $4n^2+1$ .

Square Plus One Club[]

(by Fire Christi guinto)

The "Square Plus One" Club is for numbers that are one more than a square number. Members on this club include 2, 5, 10, 17, 26, 37, 50, 65, 82, and 101.

The formula is $n^2+1$ .

Square with Spikes Club[]

(by JingzheChina) This club is for odd squares with four spikes on center of each side. Members in this club include 5, 13, 29, and 53. The owner of the club is Fifty-Three.

The formula is $(2n+1)^2+4 = 4n^2+4n+5$ .

Stellated Octagon (Type I) Club[]

Jz353a — 353 in stellated octagon (Type I) arrangement

This club is for the numberblocks which can arrange into a stellated octagon of Type One, in which all the 16 sides have the same size.

The members include 1, 29, 97, 205, 353, 541, 769, 1037, and so on.

The formula is $(4n+1)^2+4n^2=20n^2+8n+1$ .

Stellated Octagon (Type II) Club[]

Jz1061 — 1061 in stellated octagon (Type II) arrangement

(by JingzheChina) This club is for the numberblocks which can arrange into a stellated octagon of Type Two, in the original unstellated octagon of which all the 8 sides have the same size.

The members include 1, 53, 185, 397, 689, 1061, and so on.

The formula is $(6n+1)^2+4n^2=40n^2+12n+1$ .

Squares Without Corners Club[]

(by TheMainGus, expanded upon by TSRITW)

The "Squares Without Corners" Club (originally called the "Circle" Club) is a club which consists of squares that can make a square that doesn't have the 4 blocks in their corners. The members of this club are 5, 12, 21, and 32.

The formula is $(n+2)^{2}-4$ or $n^2+4n$ .

Caved Cube Club[]

The club is for numberblocks which can arrange in a cube, but every face is concave. On every face, a "pyramid" (octahedral number) is taken out, and the thickness of every side remains 2, to keep the numberblock connected.

The formula is $36n^2-16n+7$ . 827 is the owner.

Windmill/Pinwheel Club[]

(by Gelip1234)

Windmill/Pinwheel Club is for Numberblocks that can make a windmill, or a pinwheel-like shape.

The formula is $(n+3)^2-8$ , $(n+1)^2+4n$ , or $n^2+6n+1$ .

Members of this club include 8, 17, 28, 41, 56, 73, 92, 113, 136, and a bunch more.

Pumpkin Lantern Club[]

The pumpkin lantern pattern is a hollow cube of odd size, and adding One as the stem on top. All the members of Pumpkin Lantern Club are multiple of 3.

The formula is $(2n+1)^3-(2n-1)^3+1$ , or $24n^2+3$ .

The owner of this club is 219.

Diamond Club[]

This time, the club IS for Two. If you can make a perfect diamond that when rotated can still make a square, you're allowed to join this club!

Memebers include 2, 8, 18, 32, 50, 72 etc.

The formula is $2n^2$ .

Centered Square Club[]

(by Mr. Yokai, and Dozenalism and WhiteWasTheImpostor had similar ideas)

The "Centered Square" Club is for any centered squares. The owner of this club is 41. The formula is $n^2+(n-1)^2$ or $2n^2-2n+1$ .

L-Filled Square Frame Club[]

The "L-Filled Square Frame" Club is for numbers who can create a square with an odd side length hollowed out and partitioned into L-shaped holes which nest into the frame. See reference image included if the idea is hard to follow. Members of this club include 8, 19, 34, 53, and 76.

The formula is $2n^2+5x+1$ .

Honeycomb Club[]

(by ToonJaquin)

The "Honeycomb" Club is for numbers who can create a hexagonal lattice surrounding their center block. Members include Seven, Nineteen, Thirty-Seven, and Sixty-One. Thirty-Seven is the founder of Honeycomb Club.

The formula is $n^3-(n-1)^3$ , or $3n^2-3n+1$ .

Waffle Club[]

The "Waffle" Club is for numbers who can create a square with an odd side length containing the maximum number of non-connected 1x1 holes possible. Members of this club include 8, 21, 40, 65, 96 and 133.

The formula is $3n^2+4n+1$ .

Building with Windows Club[]

(by Angrycreeper123)

The 'Building with Windows' Club is similar to the 'Waffle Club' shown above, except it's for any rectangle with odd side lengths containing the maximum number of non-connected 1×1 holes possible. (canon to Numberblocks) Members of the club include: 8, 13, 18, 21, 23, 28, 29, 40, 45, 48, 63

The formula is (2x-1)(2y-1)-(x-1)(y-1) or 3xy-x-y, where x is the nth odd number of the width and y is the nth odd number of the height (for example, 7 is the 4th odd number so x and/or y would equal 4)

Cube with a Hole in Club[]

(by GenericPerson398)

The "Cube with a Hole in" Club is for numbers that can make a cube with a hole. The owner is 24. 48, 80 and 120 are also in the club.

The formula is $n^3-n(n-2)^2$ , or $4n^2-4n$ .

Star Club[]

(by ThatGuy30722)

The "Star Club" is for numbers that can make a six-pointed star. Its members are 1, 13, 37, 73, 121, 181, 253, 337, 433, 541, 661, 793, 937 and so on.

73 is the leader of the club.

The formula is $6n^2 + 6n +1$ .

Rounded Square Club (FireArrowNewer)[]

The "Rounded Square" club is for numbers that can make a square, but unfortunately missing one block in each corner, preventing them from making a perfect square. The owner of this club is FireArrowNewer's 77.

The formula is $n^{2}-4$ or $(n+2)(n-2)$ .

Heart Club[]

(by Asaki88bbff)

The Heart club is for numbers that can make a heart shape.

Members include 13, 39, 79, 133, ...

The formula is $7n^2-9n+3$ .

Jewel Club[]

(by Asaki88bbff)

The Jewel Club is for numbers that can make a jewel shape. They are also centered heptagons.

Members include 8, 22, 43, 71, 106, 148, ...

The formula is $\frac{7n^2+7n+2}{2}$ .

Truncated Square Club[]

(by Asaki88bbff)

The Truncated Square Club (or Octagon Club, in Asaki88bbff's habit) is for numbers that can make a octagon shape, or a truncated square.

Members include 12, 37, 76, 129, 196, ...

The formula is $7n^2-10n+4$ , or $7(n-1)^{2}+4(n-1)+1$ .

Wings Club[]

(by Asaki88bbff)

The Wings Club is for numbers that can make wings shape.

Members include 15, 41, 79, 129, ...

The formula is $6n^2-4n-1$ .

Double Arrow Club[]

883cc — 883 in his "double arrow" arrangement

Double Arrow Club is for numbers who are one more than twice a square. The club's leader is 579.

Members include 3, 9, 19, 33, 51, 73...

The formula is $2n^{2}+1$

Centered Hexagon Club[]

37tg — 37 in her centered hexagon arrangement

(by ThatGuy30722)

Club for numbers who can make a cube shape with a another cube number of blocks missing. The members are 7, 19, 37, 61 and 91.

Formula is $(n^2)+(n(n-1))+(n-1)^2$ , or $2n^{2}+n+(n-1)^{2}$ .

Windmill Club[]

(by Asaki88bbff)

The Windmill Club is for numbers that can make a windmill shape.

Members include 9, 21, 37, 57, 81, 109, ...

The formula is $2n^{2}+2n-3$ .

Sussy Numbers[]

Sussybakaamogusclub — An Image of 10, 40, and 90

(By Mynewaccountbcmypreviousoneinactived)

These are numbers that can make the shape of an Among Us character. The members are: 10, 40, 90, 160, and so on.

Formula: ${\displaystyle 10(x^2) }$

Cubic function clubs[]

Cubic function clubs can be written as $an^3+bn^2+cn+d$ , where $a$ , $b$ , $c$ , and $d$ are real constants.

Diminished Cube Club[]

Jz181b — 181 in his diminished cube arrangement

Asaki23 — 23 in his centered pentagonal pyramid arrangement

(By JingzheChina and Asaki88bbff)

Also called "Centered Pentagonal Pyramid Club".

This club refers to A004068 in OEIS. These numberblocks can arrange in either a diminished cube or a centered pentagonal pyramid.

The members include 1, 7, 23, 54, 105, 181, 287, 428, 609, 835, 1111, and so on. The formula is $\frac{1}{6}(5n^3+n)$ or ${\frac {5}{6}}n^{3}+{\frac {1}{6}}n$ . The owner of the club is 181.

Cube with Ponytail Club[]

(by Asaki88bbff and JingzheChina)

This club is for cubes with an extra ponytail.

The formula is $n^3+n+1$ . The members include 3, 11, 31, 69, 131, 223, and so on. The owner of the club is 223, or the "cute ponytail sister".

Cube with a "Conduit Frame" Club[]

The pattern looks like a cube with an extra frame just like "conduit frame" in Minecraft.

The members include 19, 69, 191, 433 and so on. The formula is $(2n+1)^3-(2n)^3+(2n-2)^3=8n^3-12n^2+30n-7$ . The owner of the club is 191.

Cube with Horns Club[]

The patterns looks like three horns grows up from each corner of a cube. The formula is $n^3+24$ where $n\ge 2$ .

Blossomed Cube Club[]

The pattern looks like the eight corners of a cube "blossoms". The formula is $n^3+40$ where $n \geq 4$ .

Stellated Cuboctahedron Club[]

This club is made of numberblocks who can make a stellated cuboctahedron shape.

The members include 33, 161, 457, etc.

The formula is $12n^3+12n^2+8n+1$ .

Rhombicuboctahedron Club[]

(by Asaki88bbff and JingzheChina)

This club is for numberblocks which can make a rhombicuboctahedron shape.

The members include 1, 32, 171, 504, 1117, etc.

The formula is $\frac{1}{3}(43x^3-96x^2+80x-24)$ , or ${\frac {43}{3}}x^{3}-32x^{2}+{\frac {80}{3}}x-8$

Great Rhombicuboctahedron Club[]

(by Asaki88bbff)

This club is for numberblocks which can make a great rhombicuboctahedron shape, also called truncated cuboctahedron.

The members include 1, 136, 871, 2728, etc.

The formula is $87x^3-222x^2+192x-56$ .

Centered Cuboctahedron Club[]

This club is for numbers which are centered cuboctahedral numbers (also centered icosahedral numbers), refering to A005902 in OEIS.

The members include 1, 13, 55, 147, 309, 561, 923, etc.

The formula is $\frac{1}{3}(2n+1)(5n^2+5n+3)$ or ${\frac {10}{3}}n^{3}+5n^{2}+{\frac {11}{3}}n+1$ .

Even Spiral Cube Club[]

(by Asaki88bbff)

This club is for numberblocks which can make a spiral cube shape that length is even number.

The members include 6,44,138,312,590...

The formula is $4n^{3}+4n^{2}-2n$

3D Butterfly Club[]

This club imitates the 2D butterfly pattern (one less than double step squad). This is for numbers that are one less than double a 3D step squad (tetrahedral numbers).

The owner is 239.

The formula is $\frac{1}{3}n(n+1)(n+2)-1$ or ${\frac {1}{3}}n^{3}+n^{2}+{\frac {2}{3}}n-1$ .

Windowed Cube Club[]

Jz1597 — windowed cube 1597, he is also a Fibonacci number

This club is for the 3D cubes, but windowed on each face.

The members include 27, 101, 247, 513, 947, 1597, 2511, ...

The formula is $(2n+3)^3-24n^2 = 8n^3+12n^2+54n+27$ .

Rhombic Dodecahedron Club[]

Jz369 — 369 in rhombic dodecahedron shape

Jz671 — 671 in rhombic dodecahedron shape

(by Asaki88bbff and JingzheChina)

This club is for rhombic dodecahedral numbers.

The members include 1, 15, 65, 175, 369, 671 and so on.

The formula is $n^4-(n-1)^4$ .

Mutilated Cube Club[]

(by FireArrowNewer)

This is a club for Numberblocks that can make a cube with an odd edge length with the highest possible amount of 1x1x1 non-connecting by side spaces on the cube's surface. (???)

71 is the owner of this club.

Members: 21 (27 - 6), 71 (125 - 54), 193 (343 - 150), 435, 845, 1 471, 2 361, 3 563, 5 125, 7 095, 9 521, 12 451...

The formula is $n^3-6(n-2)^2$ , or $n^3-6n^2+24n-24$ .

Ball Club[]

The "Ball" Club is for numbers that can form a "ball" shape, which can be combined with a member of the Wireframe club as to create a cube. Members of this club include 7, 32, and 81.

The formula is $(n+2)^3-(12n+8)$ , or $n^3+6n^2$ .

Swiss Cheese Club[]

The "Swiss Cheese" Club is for numbers that can form a cube with an odd side length with the maximum possible number of unexposed, non connecting 1x1x1 holes. This club is the 3D equivalent of Waffle Club. Members include 26, 117, 316, 665, and 1,206.

The formula is $7n^3+12n^2+6n+1$ .

3d Up and Down Steps Club[]

30 updownss — Asaki88bbff's 3D up and down step 30

(by Asaki88bbff)

The 3d Up and Down Steps Club is for numbers that can make a 3d up and down steps shape.2 3d steps make a this just like 2 steps make a square.

Members include 1,5,14,30,55,91...

The formula is $2n^{3}+3n^{2}+n \over 6$ .

Octahedron Club[]

(by Asaki88bbff)

The Octahedron Club is for octahedral numbers.like 2 steps make a square,2 3d up and down steps make an octahedron.

Members include 1,6,19,44,85,146... the owner is 146.

The formula is $(2n^{3}+n) \over 3$ .

Centered Octahedron Club[]

Jz377a — JingzheChina's centered octahedron 377

(by Asaki88bbff)

The Centered Octahedron Club is for centered octahedron numbers.

Members include 1,7,25,63,129,231...

The formula is $4n^{3}-6n^{2}+8n-3 \over 3$ .

Double Hexagonal Pyramid Club[]

35 double 6kujkim — Asaki88bbff's double hexagonal pyramid 35

(by Asaki88bbff)

The Double Hexagonal Pyramid Club is for numbers that can make a double hexagonal pyramid shape.like 2 steps make a square,2 cubes make a this.

Members include 1,9,35,91,189...

The formula is $n^3+(n-1)^3$ or $2n^3-3n^2+3n-1$ .

Cube Star Club[]

(by Asaki88bbff)

The Cube Star Club is for numbers that can make a 3d star shape with 6 corners.also looks like a rhombic dodecahedron(Hexagonal prism numbers).

Members include 1,14,57,148,305...

The formula is $3n^3-3n^2+n$ .

Triangular Pillar Club[]

(by Asaki88bbff)

The Triangular Pillar Club is for numbers that can make a Triangular pillar shape that every side is the same length(block).

Members include 1,6,18,40,75,126...

The formula is $n^{3}+n^{2} \over 2$ .

3d House Club[]

(by Asaki88bbff)

The 3d House Club is for numbers that can make a 3d house shape.

Members include 1,6,22,57,119,216,356...

The formula is $8n^{3}-15n^{2}+19n-6 \over 6$

Tetrahedron Hat Cube Club[]

(by Asaki88bbff)

The Tetrahedron Hat Cube Club is for numbers that can make a cube with a tetrahedron hat shape,and the length of tetrahedron's and cube's sides are same.

Members include 2,12,37,84,160,272...

272 is the owner.

The formula is $n^3+\frac{n^3+3n^2+2n}{6}$ .

Cube Made of Balls Club[]

Asaki63 balls — the cube made of 63 balls

(by Asaki88bbff)

This club is for numberblocks that can make a cube in tetrahedron&octahedron accumulation, or if change their cube blocks into balls or rhombic dodecahedrons.Every face of the cube is a centered square.

The members include 1,14,63,172,365...

The formula is $4n^{3}-6n^{2}+3n$

Oblique Tetrahedron Club[]

119blocks(corrected) — Using source material from ThatGuy30722, the 119 is an "oblique tetrahedron"

by (Saghurat Fraghraghuus)

The Oblique Tetrahedron Club is for numberblocks that can make a "oblique tetrahedron".

Members are 1, 4, 11, 24, 45, 76, 119, etc. 119 owns the club.

The formula is $n^{3}+2n \over 3$ .

(Yes it is A006527 in OEIS)

Hollow Cube Club[]

(by Bananasoft)

This club is for cube numbers that are actually empty on the inside, just like a cardboard box.

The formula is $n^3-(n-2)^3$

The members in this club are Twenty-Six, Fifty-Six, Ninety-Eight, One Hundred and Fifty-Two, etc.

Higher polynomial clubs[]

Higher polynomial clubs can be written as a polynomial of order 4 or more, i.e. $a_x n^x + a_{x-1} n^{x-1} + a_{x-2} n^{x-2} + ... + a_2 n^2 + a_1 n + a_0$ , where $a_x$ , $a_{x-1}$ , ... $a_0$ are real constants, and $x$ is a whole number that's larger than 3.

Tesser Actors[]

(by Inthescar) Blocks that are numbers to the fourth power. Numbers: 1, 16, 81, 256

4D Step Club[]

Also called "5-cell" club.

This club is for 5-cell numbers. Members include 1, 5, 15, 35, 70, 126, 210, 330, 495, 715, 1001 and so on.

The formula is $\frac{n(n+1)(n+2)(n+3)}{24} = \left(\begin{array}{c}n+3\\4\end{array}\right)$ , or ${\frac {n^{4}+6n^{3}+11n^{2}+6n}{24}}$ .

16-Cell Club[]

(by Asaki88bbff)

The 16-Cell Club is for 16-cell numbers.

Members include 1, 8, 33, 96, 225, 456 and so on.

456 is the owner of the club.

The formula is ${\frac {n^{4}+2n^{2}}{3}}$ .

Another 16-Cell Club[]

(by Asaki88bbff)

This club is for numberblocks that can make a regular 16-cell shape by blocks, different from 456's. This kind of 16-cell is gotten by cutting a hyper cube's 8 vertices.

The members include 1,8,41,136,345,736...

The formula is $(2n^{4}-2n^{3}+n^{2}+2n)/3$

Triangular-antitegmatic Icosachoron Club[]

Jz211a — 4D triangular-antitegmatic 20-cell arrangement of 211

Jz781b — 4D triangular-antitegmatic 20-cell arrangement of 781

Triangular-antitegmatic icosachoron is also called triangular-antitegmatic 20-cell, and is the 4D version of rhombic dodecahedron.

This club is for triangular-antitegmatic icosachoral numbers.

Members include 1, 31, 211, 781, 2101 and so on.

The formula is $n^5-(n-1)^5$ .

Hypercube Club[]

Asaki4d-1296 — Asaki88bbff's hyper cube 1296

(by Ultralis36)

The "Hypercube" Club it is only for numbers that can make a hypercube. Members include 1, 16, 81, 256, and 625.

The formula is $n^4$ .

Cubes Made of Cubes Club[]

(by A user that likes plants)

For cube-times-cube numbers (that aren't 1) like 64 and 729.

The formula is $n^6$ .

Rectangular Prism Club[]

Where the idea came from.

This club is for Numberblocks who can make a rectangular prism.

The members are: 12, 18, 24.

Decaract Club[]

(by Onebillionn9999)

For square^5 numbers (not including 1) like 1,024, 59,049 and 1,048,576.

The formula is $n^{10}$ .

Squares Made of Squares Club[]

(by Getinthegroovewith36

If you're a square-times-square number (except 1), then you can join this club. Members are 16, 36, 81, 256, 400, 900, and 10,000. 256 is the most active.

The formula is $n^2*n^2$ .

Dodecagonal Club[]

(by Testy2049)

This club is for Numberblocks who represent/can make a dodecagon (12-sided polygon). The owner of this club is Twelve.

Members of this club include: One, Twelve, Thirty-Three, Sixty-Four, One Hundred and Five, One Hundred and Fifty Six and so on.

The formula for this club is $1\div 2\times \eta \times 10-8$ .

Exponential clubs[]

Exponential clubs can be written as $a^n$ , where $a$ is a real constant.

Doubler Club[]

(by Dariber, and Dark Shadow King, JGVN Joey Forty Eight, Activate had similar ideas)

The "Doubler" Club is a club for doublers, like Dariber's 0.5, 1, 2, 4, 8, 16, 32 and 64.

The formula is $2^n$ , where $n\in\mathbb{Z}$ .

Members: 0.5, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192 and 16,384.

Dozenalism has a similar idea, but is only for non-negative powers (i.e. $n \in \N$ ), and is called "Doubling Club".

ButterBlaziken230 also has a similar idea and works the same as Dozenalism's, except is called "Folding Club". 2,048 is the leader of the club, too.

Triple Club[]

(by Fernandez0907) The "Triple" Club is a club for numbers who are powers of three. The members are: 3, 9, 27 and 81.

The formula is $3^n$ .

Magnitude Masters Club[]

(by Tardigradelover255‎)

This club is for numbers who are powers of ten. The current figured out members are: 1, 10, 100, 1,000, 10,000, 100,000, 1,000,000, 10,000,000, 100,000,000 and 1,000,000,000.

The formula is $10^n$ , where $n\in\mathbb{Z}$ and $n\geq 0$ .

Baguenaudier Club[]

This club is for the count of steps of baguenaudiers (or Chinese Rings) of various size. Since baguenaudiers are related to the Gray code, the club can also discribed as, the club for numbers whose Gray code only contains 1, i.e. the binary form is alternating 1 and 0. See A000975 in OEIS.

The members include 1, 2, 5, 10, 21, 42, 85, 170, 341, 682, 1365, etc.

Since the default size of baguenaudier is 9 ("九连环" in Chinese), the owner of this club is 341.

The formula is $\frac{2}{3}\cdot 2^n - \frac{1}{2} - \frac{(-1)^n}{6}$ .

Menger Sponge Club[]

(by JiaGbon1234)

This club is for numbers who can make a "Menger Sponge" shape.

The members are: 1, 20, 400, 8000. The leader is 20.

The formula is $20^n$ .

Multi-variable Clubs[]

Multi-variable clubs are clubs which formulas have two or more variables.

Difference of Cubes Club[]

Numberblocks which can be difference of two cubes. The formula is $a^3-b^3$ or $(a-b)(a^2+ab+b^2)$ where $a > b$ and $a,b\in\N$ .

999 is the owner of this club because he can be written as difference of cubes in two ways: 1728-729, or 1000-1.

Twisted Cube Club[]

Numberblocks which can be arranged in the pattern on the left.

This 803 is made of four cuboids, 8x8x8, 8x8x3, 8x3x3, and 3x3x3.

The formula is $a^3+a^2b+ab^2+b^3$ , or $(a+b)(a^2+b^2)$ , with $a,b\in\N$ . The owner of this club is 803.

Cube with a Bizzare Octant Club[]

A club for "even cubes, but one octant in different size".

The formula is $7a^3+b^3$ where $a,b\in\N^+$ and $a \ne b$ . The owner is 876.

Crown Club[]

(by DrinkingDragonJuice)

Numbers with a wide odd number with a separated number of blocks on top can join.

The blocks can have:

Five wide being multiplied with separated blocks on top.
Numbers having the separated blocks even taller.

The formula is $c(2n+1)+n+1$ , where $c\in\N$ .

Both can be possible, but the five wide would have to be longer than that to fit taller separated blocks in. The club's members are: 5, 8, 11, 13, 14, 17, 18, 20, 23 and 26. Since 8 made some kind of normal crown, he is the owner.

Squareful Club[]

(by Dozenalism)

Interested in squares but not exactly a square? You're welcome to join if you're divisible by a square (except 1)!

"Square with a hole" numbers are all in this club, as they are all divisible by 4.

Members: 4, 8, 9, 12, 16, 18, 20, 24, 25, 27, 28, 32, 36, 40...

Numbers in this club can be written as $cn^2$ , where $n>1$ and $c\in\N$ .

Twos and Threes Club[]

(by Dozenalism and JingzheChina)

also named "3-Smooth Club". The founder is Ninety-Six.

If your factorization only consists of Twos and Threes.

Numbers in this club can be written as $2^x\cdot3^y$ , where $x,y \geq 0$ and $x,y\in\Z$ .

(x)ler Club[]

The "(x)ler" Club is like the Doublers Club, except it's instead triple, quadruple, quintuple, etc.

The formula is $x^{y}$ , where $x>1$ , $y>1$ , and $x,y \in \mathbb{N}$ .

Two-Square Club[]

(by TSRITW)

The "Two-Square" Club is for numbers that can be written as sums of two perfect squares.

Members: 1, 2, 4, 5, 8, 9, 10, 13, 16, 17, 18, 20, 25, 26, 36...
(numbers in bold are perfect squares)

Numbers in this club can be written as $a^2+b^2$ or $(a \pm b)^2 \mp 2ab$ , where $a, b \in \Z$ and $a,b \geq 0$ .

Times Table-Included Club[]

This club is for any Numberblock who can make at least one rectangle or square whose width and height are both height are both natural numbers between 1 and 10 (inclusive).

Numbers in this club can be written as $ab$ , where $a,b \geq 1, \leq 10$ and $a, b \in \Z$ .

This club has tiers depending on how many qualifying rectangles and squares a given number can make, with said number being its tier number. For example, 14 can be 2×7 or 7×2, and is thus Tier 2.

Cuboid Club[]

(by AllEnginesReadyToGo)

The "Cuboid" Club is for numbers that are a product of three natural numbers that are larger than one. Members include Eight, Twelve, Sixteen, Eighteen, Twenty & Twenty-Four.

Numbers in this club can be written as $xyz$ , where $x,y,z > 1$ and $x,y,z\in\N$ .

Non-Three-Square Club[]

(by Saghurat Fraghraghuus)

The club is for blocks which can't be split into at most three squares(if you consider 0 as a square,"at most" can be removed). 7, 15, 23, 28, 31 ,39 are in the club.

It's A004215 in OEIS.

The formula is $4^\alpha (8k + 7)$ where $\alpha ,k\in \mathbb {N}$ .

Summation clubs[]

Summation clubs are clubs which formulas can be written as summations. Note that some of these clubs are multi-variable.

Partial Step Squad Club[]

(by TSRITW, inspired by Dozenalism)

The "Partial Step Squad" Club is a club for partial step squads, where each number can be written as a sum of more than one consecutive natural numbers, e.g. 3+4+5=12, so Twelve is a part of this club.

In fact, every natural Numberblock is in this club, except powers of two.

The formula can be written as $\sum_{x=c}^{n} x$ , where $c\in\N$ and $c\ne n$ .

Two-Step Squad Club[]

(by Alccap)

Basically the Step Squad Club but adding sequence even numbers, e.g. 2+4+6=12, so Twelve is a part of this club.

Members: 2, 6, 12, 20, 30, 42, 56, 72, 90, 110...

This club is also known as the "Not Quite Square" Club, since the members' squarest rectangles get closer and closer to 1:1 as they get bigger.

The formula can be written as any of these:

$n(n+1)$
$2\sum_{x=1}^{n} x$
$2T_n$

where $T_n$ refers to the $n$ ^th triangular number.

Base Step Club[]

(by Arandomusernamesoicangetin)

Members of this club have to be able to make a step squad with each step being the same number. For example, 110. Each step is a two and it goes from two to twenty.

The formula can be written as any of these:

$\frac{cn(n+1)}{2}$
$c\sum_{x=1}^{n} x$
$cT_n$

where $c\in\R$ , and $T_n$ refers to the $n$ ^th triangular number.

TSRITW has a similar idea, but with the added condition of $c\neq1$ , and is called "Pseudostep Club".

Steps With a Hole Club[]

(by Lookiecookie0505, and Fire Christi guinto had a similar idea)

The "Stairs With a Hole" Club is for numbers who can make Step Squad shapes with a hole the shape of the Step Squad four steps smaller. Members of this club include 14, 18, 22, 26, and 30.

The formula can be written as any of these:

$4n-6$

$\frac{n(n+1)-(n-4)(n-3)}{2}$

$\sum_{x=(n-4)}^{n} x$

$T_n - T_{n-4}$

where $n>4$ , and $T_n$ refers to the $n$ ^th triangular number.

Butterfly Club[]

(by ThatGuy30722)

131tg — 131 in her butterfly arrangement

Club for numbers who can make a butterfly that consists of two step squads (with one of them having one block missing) joined by their corners. Members are 5, 11, 19, 29, 41, 55, 71, 89, 109, 131, 155 and 181.

The formula is $n(n+1)-1$ .

Tetrahedron Club[]

(by Dariber)

The "Tetrahedron" Club is a club for tetrahedral numbers. The first five members are 1, 4, 10, 20 and 35.

The formula can be written as any of these:

$\frac{n(n+1)(n+2)}{6}$
$\sum_{x=1}^{n} x(n-x+1)$
$\sum_{x=1}^{n} T_x$

where $T_n$ refers to the $n$ ^th triangular number.

(ButterBlaziken230 has a version of this club called "Tetra Squads", while Inthescar has one called Tetrisers.)

Square Stackers Club[]

(by ButterBlaziken230)

The "Square Stackers Club" is a club for numbers that are made up of a list of squares. For example, Five is a Square Stacker due to being 1 + 4. Fourteen is due to being 1 + 4 + 9. Thirty is the fourth member due to being 1 + 4 + 9 + 16, making Fifty-Five the fifth member being made up of 1 + 4 + 9 + 16 + 25.

The formula can be written as any of these:

$\frac{n(n+1)(2n+1)}{6}$
$\sum_{x=1}^{n} x^2$

TSRITW has a similar idea, but it was called the "Square Pyramid Club".

Perfect Pyramid Club[]

Similar to the Square Stackers Club, but it makes a perfect pyramid, aka pyramids that are completely centered and don't have any further blocks to add on (thus, 83 can't be apart of this club). The odd block members (excluding 1) include 10, 35, and 84, while the even top members (excluding 4) include 20, 56, and 120.

The formulas can be written as

Odd Blocks:
$\sum_{x=1}^{n} (2x-1)^2$
Even Tops:
$\sum_{x=1}^{n} (2x)^2$

Sums of Cubes Club[]

(by TSRITW)

The "Sums of Cubes" Club is a club for numbers that are made up of a list of cubes. Members include 1, 9, 36, 100, and 225.

This club is also known as the "Squares of Step Squads" Club, since each member is equal to the square of a triangular number. TSRITW himself proved it with mathematical induction.

The formula can be written as any of these:

$\sum_{x=1}^{n} x^3$
$\bigg(\frac{n(n+1)}{2}\bigg)^2$

Explosion Club[]

The "Explosion" Club is for numbers that can make a cube... with some additional blocks on it, unfortunately, preventing them from making a perfect cube; however, it must be in the middle, or otherwise they can't join; they also have to end the "explosion" with a one or four on each tip. Members include 33, 88, 185, 336, and 553.

The formula can be written as any of these:

Odd Cubes:
$(n+2)^3+6\sum_{x=1}^{\frac{n+1}{2}} (2x-1)^2$
Even Cubes:
$(n+2)^3+6\sum_{x=1}^{\frac{n}{2}} (2x)^2$

Pentatope Club[]

(by C1932)

The "Pentatope" Club is a club for pentatope numbers. The first five members are 1, 5, 15, 35, and 70.

The formula can be written as any of these:

$\frac{n(n+1)(n+2)(n+3)}{24}$
$\frac{(n+3)Te_n}{4}$
$\sum_{x=1}^{n} Te_x$

where $Te_n$ refers to the $n$ ^th tetrahedral number.

Octagon Club[]

By @FireArrowNewer

This is a club for every numberblock that can make an octagon.

Formula:

${\displaystyle ((n^2)*5)+(\sum_{k=1}^a*4), a=n-1}$

"Adding Previous Terms" Clubs[]

"Adding previous terms" clubs involve having a term being the sum of two or more previous terms, Fibonacci-style.

Bunny Club/Fibonacci Squad[]

(by TSRITW, Inthescar, and JingzheChina)

The "Bunny" Club is for the Fibonacci numbers (they originated from a riddle about the population of rabbits). The founder of this club is 34, and 89 is the most active member of the club.

The club badge of Bunny Club is a blue pentagonal icon with a bunny head on it. The reason why the badge is pentagonal is that, the general formula of Fibonacci sequence includes the square root of five, and Five herself is also a member of this club.

Jz89a — Eighty-Nine with her club badges

The formulas are

$x_1=1$
$x_2=1$
$x_n = x_{n-1} + x_{n-2}$

or

$x_n = \frac{1}{\sqrt{5}} \left[\left(\frac{1+\sqrt{5}}{2}\right)^n - \left(\frac{1-\sqrt{5}}{2}\right)^n\right]$

Curious Animators has a similar idea, but it's called the "Fibonacci Sequence" Club. The owner of this club is Curious Animators' 34.

Leapfrog Club/Lucas Club[]

(by TSRITW and Inthescar)

The "Leapfrog" Club is for the Lucas numbers, and is the rival to the Bunny Club. The owner of this club is 47.

The formulas are

$x_1=2$
$x_2=1$
$x_n = x_{n-1} + x_{n-2}$

Pell Number Club[]

(by Saghurat fraghraghuus)

The "Pell Number" Club is for numbers which are Pell numbers (OEIS A000129).

The members are 1, 2, 5, 12, 29, 70, 169, etc. 29 owns this club.

The formula is $(1+{\sqrt {2}})^{n}-(1-{\sqrt {2}})^{n} \over 2{\sqrt {2}}$ .

And the recurrence relation is that $a_{n+1}=2a_{n}+a_{a-1}$ where $n\ge 2$ .

Not Pell Number Club[]

(by Saghurat fraghraghuus)

The Club is for numbers which are related to Pell numbers but not Pell numbers (OEIS A001333).

The members are 1, 3, 7, 17, 41, 99, 239, etc. 41 owns this club.

The formula is $(1+{\sqrt {2}})^{n}+(1-{\sqrt {2}})^{n} \over 2$ .

(Yes This club and Pell Number Club have something in common like same recurrence relation)

Quadribonacci Club[]

This club follows the same pattern as Fibonacci, but you add the previous 4 terms.

The members are 1, 2, 4, 8, 15, 29, 56, 108, 208, 401, 773, 1490, 2872, 5536, 10671, and so on.

Prime-related Clubs[]

Prime-related clubs are clubs related to prime numbers.

Mersenne Club[]

(by Dozenalism and JingzheChina)

Mersenne Primes only. You may join if you're a prime that is one less than a doubler. (Formula: $2^n-1$ ). One Hundred Twenty-Seven is the leader of the club, as the largest known doubly Mersenne prime, and the smallest triply Mersenne prime, as well as the 31^st prime (which Thirty-One is also Mersenne!). What's more, $2^{127}-1$ is also a Mersenne prime.

Dozenalism's design of the club badge is a black 1:2 rectangle with one small square part missing, with a gold letter "M" on it (like the logo for the Ministry of Magic in Harry Potter).

JingzheChina's design of the club badge is a round and violet badge, with a violet capital letter "M".

Double Mersenne Club[]

(by TheDucker123456) The Mersenne Club but Doubled. The Formula is $M_{M_{p}}=2^{2^{p}-1}-1$

The Design is JingzheChina's style.

Five Fingers Club[]

This is a finite club, which contains only five members.

Mathematical References[]

This club is based on A352057 in OEIS. Apply the iteration $a_{n+1} = 2 a_n + 1$ to $a_1=2$ , and the first five terms are all primes, while the prime property cannot insist for so long when apply to other prime initial values ―- until 89. Thus the finite sequence may have some meanings.

FiveFingers Pattern — A kind of pattern of Five Fingers Club by Asaki88bbff

Introduction of the Club characters[]

Since this club contains only five members which accords with the number of Five, five founds this club named by her five finger, where Two for the thumb, Five herself for the index finger, Eleven for the middle finger, Twenty-Three for the ring finger, and Forty-Seven for the pinky.

In this club, Twenty-Three really figures himself out, for the golden ring put on his body, which refers he is the "ring finger". And Forty-Seven figures herself out to be a cute girl who loves pink color and likes to say "Pinky-pinky".

Fermat Prime Club[]

Club for Fermat primes, or primes of formula $2^{2^n} + 1$ . Up to now, there are only five members in this club.

Except Three and Five, all members likes to paint, but the styles are distinct.

The members include 3, 5, 17, 257, 65537.

Primorial Club[]

(by JiaGbon1234)

This club is for numbers that are primorials. Primorial is just factorial but with primes. For example: $7\#=2\times3\times5\times7=210$ .

Its members are 2, 6, 30, 210, 2310. The club leader is 30.

The formula is $p_n\#$ or $2\times3\times5\times\cdots\times p_n$ or $\prod_{i=1}^np_i$ , where $p_i$ is the i-th prime.

Partners in Prime Club[]

(by TheOrion1)

The Partners in Prime Club is a club for Numberblocks who are doubles of prime numbers. It is A100484 in the OEIS.

Balanced Prime Club[]

Balanced Prime Club is for balanced primes. Members include 5, 53, 157, 173, 211...

The formula is $p_n = {{p_{n - 1} + p_{n + 1}} \over 2}.$

Quiet Primes Club[]

(by Asaki88bbff)

The Quiet Primes Club is for prime numbers that are both semiprime+1 and 12's multiple-1.in Asaki88bbff's setting,their personalities are quiet.they can't make 2d highly symmetric shapes by their blocks,but they are good at spiral patterns！

Members include: 11,23,47,59,83,107,167...

Short Period Primes Club[]

(by Asaki88bbff)

The Short Period Primes Club is for short period prime numbers,if a is prime,and the length of period 1/a<a-1,then a can join this club.

Members include 3,11,13,31,37,41...

Sophie Germain Club[]

This club is for Sophie Germain primes.

Members include 2, 3, 5, 11, 23, 29, etc...

Wieferich Prime Club[]

1093blocks — 1093, one of two Wieferich primes (using source material from ThatGuy30722)

(by Saghurat_Fraghraghuus)

The club is for Wieferich primes.

A Wieferich prime is a prime (as $p$ ) which satisfies $2^{p-1}\equiv 1(\mathrm {mod} \ p^{2})$ .

Up to now, there are only two members in the club. They are 1093 and 3511.

It's A001220 in OEIS.

Prime Steps[]

By NmbrblcksFan

It is like adding primes

The members are: 2, 5, 10, 17, 28, 41, 58, 77, 100, 129, 160, 197, 238, 281, 328, and more.

Balanced Prime Steps[]

This club is for Numberblocks who are the sum of the first $n$ balanced primes. Members include 5, 58, 215, 388, 599...

Prime Squares[]

This club is for squares of prime numbers. Every Numberblock in this club has 3 factors. This is a sub-club of both Square Club and Semiprime Club

Members include 4, 9, 25, 49, 121, etc.

Prime Cubes[]

This club is for cubes of prime numbers. Every Numberblock in this club has 4 factors, although they are not semiprimes.

Members include 8, 27, 125, 343, 1331, etc.

Array Clubs[]

Array clubs are clubs that revolve around their members' factors (divisors).

Loop-the-Looper Rectangles Club/Ultra Rectangle Club[]

(by ButterBlaziken230 and Inthescar, Loop-the-Looper name created by Objectify)

The "Loop-the-Looper Rectangles Club" is an advancement of the Super Rectangle Clubs. It is given to Numberblocks with more than 10 factors. Butter's Forty-Eight is the owner of the club.

Members: 48, 80

Semi-Primes Club[]

(by ButterBlaziken230 and Inthescar)

The "Semi-Primes" Club is an advancement of the Prime Club. It is given to Numberblocks that can only make rectangles that are either prime positions or rectangles that have width and height numbers that are both prime. Butter's Thirty-Eight is the owner of the club. In Butter's fanmade Season 9 episode "Semi-Primes", the club is discovered, where Thirty-Three, Thirty-Four and Thirty-Nine, all being Semi-Primes, figure themselves out.

Royal Rectangles Club[]

(by Dozenalism)

Largely Composite Numbers ONLY! Only the most rectangly numbers can enter. Five Thousand and Forty is the owner of the club.

Gold members (SHCNs): 2, 6, 12, 60, 120, 360, 2520...

Silver members (HCNs that are not SHCNs): 4, 24, 36, 48, 180, 240, 720...

Bronze members (LCNs): 3, 8, 10, 18, 20, 30, 72, 84, 90, 96...

Sorry Forty, despite your obsessions with rectangles, you can't join, as Thirty-Six beats you in number of divisors.

Lighthouse Club[]

(by Asaki88bbff)

If a number is more rectangly than the last doubler before it,then this number can join this club. For example,24 has 8 factors,and last doubler 16 has 5 factors,8>5,so 24 is a lighthouse number.

Members include:6,12,18,20,24,28,30,36...

Square-Free Club[]

(by Nayuta Ito)

It is given to Numberblocks that are not divisible by any square number except 1. It is the complement of Squareful Club. Two Hundred And Ten is the owner of the club.

Hyper Rectangle Club[]

(by Nayuta Ito)

It is given to Numberblocks that have so many factors that their array display can make a super rectangle. To be exact, the factors must be arranged in 6 ways or more satisfying the following condition:

It is arranged in a rectangle.
For any number N, If you multiply N to a factor and the result is still a factor, you will always get the result in the same position relative to the original factor.
The left-top corner must be 1.

For example. 60 is a Hyper Rectangle because its factors can be arranged like these:

(12x1)

1 2 4 3 6 12 5 10 20 15 30 60

x2: 1 element right, x3: 3 elements right, x5: 6 elements right

(6x2)

1 2 4 3 6 12
5 10 20 15 30 60

x2: 1 element right, x3: 3 elements right, x5: 1 element down

(4x3)

1 3 5 15
2 6 10 30
4 12 20 60

x2: 1 element down, x3: 1 element right, x5: 2 elements right

(4x3)

1 5 3 15
2 10 6 30
4 20 10 60

x2: 1 element down, x3: 2 elements right, x5: 1 element right

And their transposition.

Composite Club[]

(by JacobHarrington18 Club for numbers that have more than two factors.

The formula is $4y(x+y)+2x-1$ or $4y^{2}+4xy+2x-1$ for all positive integer values of $x$ and $y$ .

Legendary Rectangle Club[]

(by [[IckyVikcy]], also known as MisterBloks)

A legendary rectangle is a number n which it has more than 30 factors.

Members are

720
840
1008
1200
1260
1440
1680
1800
2016
2520
And more.

Divisor-related Clubs[]

Divisor-related clubs is the clubs which related to the properties of divisors, e.g. sum of proper divisors.

Perfectionist Club[]

This club is for numberblocks the sum of whose divisors equals themselves, or called perfect numbers.

Up to now, all the known perfectionists are step squads of order Mersenne primes.

The members include 6, 28, 496, and so on. The owner of the club is 496.

Couple Club[]

Warning: Join this club in PAIRS only.

This club is for amicable number pairs, i.e. two distinct numberblocks related in such a way that the sum of the proper divisors of each is equal to the other numberblock. If the two fulfilled this condition, they become a couple and join the club together.

The owners of the club are 220 and 284.

Base-specific clubs[]

Base-specific clubs are clubs that only work with a specific base.

Ell Leaders Club[]

(by ButterBlaziken230) The Ell Leaders club is a club for Dozenalblocks (Numberblocks in base 12) that are multiples of Ell (11 in base 10). That means Ell, Do-Dek and Twendy-Nine are examples of members. The formula is $\Epsilon n$ , where E represents the duodecimal digit for eleven.

Procrastinators Club[]

(by Yamato Yamamoto)

The Procrastinators club is a club for Dozenalblocks whose Numberlings refer to the last moment of a calendar date (similar to 23:59). That means Doh-El (1E), Gro-Elzy-El (1EE), Mo-Gro-Elzy-El (1EEE), are examples of members. E represents the duodecimal digit for eleven. The formula is $2(10^{n})-1$ .

Numberling-specific Clubs[]

Clubs where the members' Numberlings are significant.

Monochromic Step Squads Club[]

A352057 in OEIS. The club includes only the step squads whose non-zero digits are identical. The members are 1, 3, 6, 10, 55, 66, 300, 666, 990, 3003 and so on. The owner of this club is 666.

Palindrome Pals Club[]

(by ISNorden)

For numerical palindromes. (My own version of the club excludes single-digit numbers as a so-called "trivial case".) Eleven and her multiples leads the Palindrome Pals.

Two-Way Primes Club[]

(by ISNorden)

For emirp numbers – primes (with two or more digits) that are not palindromes, but remain prime when the digits are reversed. Thirteen and Thirty-One lead this club together; other pairs of members include {17, 71} and (79, 97}.

Repeaters Club[]

(by ISNorden and JingzheChina)

For repdigit numbers – numbers written with repeated copies of one digit. Eleven leads the Repeaters' Club; 22 and 55 are the next highest figured-out members.

Formula: $d\cdot\frac{10^n-1}{9}$ , where $d=1,2,3,4,5,6,7,8,9$ .

All-Sevens Club[]

(by Snowfirefly and JingzheChina)

This club is for numberblocks whose numberlings are all sevens! Rainbow lovers!

Formula: ${\frac {7(10^{n})-7}{9}}$

Flip-Flop Friends[]

(by ISNorden)

For strobogrammatic numbers – numbers whose digits read the same upside-down. Zero leads this club; other members include 1, 8, 11, 69, and 96.

33...331 Club[]

(by Saghurat Fraghraghuus)

The club is for blocks of numbers which can be expressed as 33...331.

The first seven members are primes, but the eighth member (333333331) can be divided by 17.

It's A033175 in OEIS and the formula is ${\frac {10^{n+2}-7}{3}}$ .

Decimal point clubs[]

The "Decimal Point" Club is for any numbers that utilize a decimal point. "Decimal Point" Clubs encompasses a more specific placement; for example, the Tenths, the Hundredths. 0.5 is the owner of all of them.

Decimal Club[]

(by ElProXXX_Gamer)

This club is only for decimal numbers like 1.24, 87.1, 0.24, 918.09.

Repeating Decimal Club[]

Like it states, the "Repeating Decimal" Club is for any decimal numbers that are stuck in a repetend (infinitely repeating digits). The leader of this club is currently 1/7, or represented in decimals, $0.\overline{142857}$ .

Fractions club[]

(by ThirtyTwo 32)

Requires a decimal point and must NOT be irrational.

One - Third leads this club.

Recurring Decimal Club[]

(by Forty-Eight, Activate!)

This is a club for numbers where the same decimal place is repeated infinitely.

Members include 1/3, 2/3, 1/9, 1/6

1/3 is the leader.

Other clubs[]

Some other clubs that don't really fit in any of the above.

Finite Projective Plane Club[]

Mathematical theories[]

If a number is the count of points/lines of a finite projective plane, then the corresponding numberblock is a member of this club. The members fit in the formula $n^2+n+1$ , where $n$ is the order.

However, not every order is available for a finite projective plane. If the order is a power of a prime (e.g. 1, 2, 3, 4, 5, 7, 8, 9, 11, etc.), then we can easily construct the projective plane by the corresponding finite field. That is to say, 3, 7, 13, 21, 31, 57, 73, 91, 133, etc. is members of the club.

But if the order is not a power of prime, then we have not found an instance yet. We have already proved that projective planes with order 6 and 10 does not exist, thus 43 and 111 are not members of the club. However, we don't know whether 157 (i.e. order 12) is in this club up to now.

Numberblocks Club[]

The founder of the club is 871, since she is for that of order 29, and 29 stands for clubs^{[clarification needed]}.

The club badge is a triangular Fano plane logo, where the points of the plane is colored in rainbow.

273 is the most active member in this club, since many divisors of her (to be more accurate, ALL divisors except 1 and 39) are members of the club. She even has a Fano plane logo on her body.

Heegner Club[]

This club is for Heegner numbers.

This is a finite club, only including nine members: 1, 2, 3, 7, 11, 19, 43, 67, 163. 163 is the owner.

Pentagon Club[]

(by BeepsterOfficial)

The Pentagon Club is for pentagonal numbers. Thirty-Five owns this club.

Negative Club[]

The "Negative" Club is the exact opposite of the "Made of Ones" Club. Negative One is the owner of this club.

The formula is $n < 0$ , where $n\in\mathbb{Z}$ .

Half Club[]

(By Dorimartiez5)

The "Half" Club is for numbers that have 1/2 or 0.5 on it's name. Half is the owner of this club.

The formula is $n-\frac12$ where $n \in \N$ .

"Smolface" Club[]

(By Dozenalism): Figured-out numbers that have a "smaller face" than other numberblocks. According to the current "smolfaces",

To join, a Numberblock must:

Be greater than 22 ( $n>22$ )
Be a prime, squarefree semiprime or a cube of a prime ( $\sigma_0(n)\subset\left \{ 2, 4 \right \}$ )
Not be a step squad ( $\sqrt{8n+1}\not\in\mathbb{Z}$ )

Partition Club[]

(by NumberblocksStuff)

This club is for numbers that are in the sequence of partition function.

The formula is $p(n)$ .

Members: 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42.

Question Mark Club[]

(by Nara Sherko)

This club is for numbers that can make a ? shape.

The formula is $n < 8$ .

Factorial Club[]

(By JiaGbon1234)

This club is for numbers that are factorials, i.e. product of integers from 1 to n. The factorial symbol is the exclamation point (!). For example: 6! = 1 x 2 x 3 x 4 x 5 x 6 = 720. It's basically step squads but with multiplication.

Its members are 1, 2, 6, 24, 120, 720, 5040. The leader is 6.

The formula is $n!$ , or $1\times2\times3\times\cdots\times n$ , or $\prod_{i=1}^ni$ .

Ex-Zero Club[]

This club is for iterations of 0 and the known hyper-zeroes that exist.

All members as of now are: _(-1), 0, Half-null (0/2), Hegirondo (?), Arrunoro (?), Kodanoro (?), Jiwanoro (?), Gihenoro (?), Tutanoro (?), Branoro (?), Underscore (?), 0.0, -0.

*a full list can be found here:

Irrational Club[]

This club is for fanmade irrational Numberblocks. Its leader is the square root of Two.

So Much More to Explore Club[]

This club is for all numbers who are factors of 97,104 or multiples of the factors of 97,104 (excluding 1) who are less than 97,104.

Complex Club[]

This club is for fanmade complex Numberblocks. Its leader is i (the square root of negative one).

Square of imaginary numbers Club[]

(by Vista-BSOD

This Club is for square of imaginary numbers, but haven't -1, like -4, -9, -16, ect. Its leader is -4.

The formula is $[(n+1)i]^{2}$ .

Dicey Sixes[]

(by TheWreckingBall78)

This club is for Numberblocks that are multiples of sixes.

The Three Semiprimes Club[]

(by Connorclarke107)

This club is for trios of consecutive semiprimes.

Members include 33, 34, 35, 85, 86, 87...

Not Made of Ones Club[]

(by 01ZanderBanks01)

The Not Made of Ones Club is for Numberblocks that aren't made out of ones (i.e. natural numbers). This club is made for Pi and Zero.

Catalan Club[]

(by Nayuta Ito)

This club is for Numberblocks that are Catalan numbers.

Its members are 1, 2, 5, 14, 42, 132, 429, and so on. 42 is the leader of the club.

5 Starter[]

(By Ramonthefunway)

This club is for numberblocks with a 5 at the left.

The formula is 50.

Fifty-Nine owns this club.

Members include 5, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 500-599, etc.

Tournament Club[]

(by Connorclarke107

This club is for Numberblocks who are 11 times a doubler. The club's leader is 44.

Members include 11, 22, 44, 88, 176, 352, 704, etc.

The formula is $2^n*11$

Tropical Club[]

(By Ramonthefunway)

This club is for multples of ten plues seven.

197 owns this club.

The formula is $10n+7$ .

Members include 17, 27, 37... etc.

Twelve Divisor Rectangle Club[]

(By User:Ramonthefunway)

This club is only for multiples of One, Two, Three, Four, Five, Six, Seven, Eight, Nine, Ten, Eleven, Twelve, Thirteen, Fourteen, Fifteen, Sixteen, Seventeen, Eighteen, Nineteen, Twenty, Twenty-One, Twenty-Two, Twenty-Three, Twenty-Four, Twenty-Five, Twenty-Six, Twenty-Seven, Twenty-Eight, Twenty-Nine, Thirty, Thirty-One, Thirty-Two, Thirty-Five, Thirty-Six, Forty, Forty-Two, Forty-Five, Forty-Nine, Fifty, Fifty-Five, Sixty, Sixty-Four, Seventy, Eighty, Eighty-One, Ninety, Ninety-Nine, or One Hundred.

The members are 60, 72, 84, 90, 96, 108, 126, 132, 140, 150, 156, 160, 200, 204, 220, 224, 228, 234, 260, 276, 294, 306, 308, 315, 340, 342, 348, 350, 352, 364, 372, 380, 392, 414, 416, 444, 460, 476, 486, 490, 492, 495, 500, 516, 522, 525, 532, 544, 550, 558, 564, 572, 580, 585, 608, 620, 636, 644, 650, 666, 675, 693, 708, 726, 732, 735, 736, 738, 740, 748, 765, 774, 804, 812, 819, 820, 825, 836, 846, 850, 852, 855, 860, 868, 876, 884, 928, 940, 948, 950, 954, 968, 975, 988, 992, 996, etc.

The formulas are $an$ , where $a=2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,35,36,40,42,45,49,50,55,60,64,70,80,81,90,99,100$ .

Universal Club A[]

This club is for members who are in 15-theorem.

Members includes 1, 2, 3, 5, 6, 7, 10, 14, 15, and the leader is 15.

Universal Club B[]

Like Universal Club A, this club is for members who are in 290-theorem.

Members includes 1, 2, 3, 5, 6, 7, 10, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 34, 35, 37, 42, 58, 93, 110, 145, 203, 290, and the leader is 290.

Carmichael Club[]

The club is for blocks of Carmichael numbers (or called absolute pseudoprimes) who (as $c$ )satisfy $a^{c}\equiv a(\mathrm{mod}\ c)$ where $a \in \Z$ but is not a prime.

561blocks~absolutePseudoprime~ — 561 is the leader of Carmichael Club (Using ThatGuy30722's source material)

The members are 561, 1105, 1729, etc., and the leader is 561.

It's A002997 in OEIS.

(Lowest Order) Perfect Squared Square Combiner Club[]