List of Numberblock Clubs/Fanmade

This gallery is for fanart! "Wait, I know what this gallery needs: your art!" — Seventeen This gallery is dedicated to fanart. None of the pictures are official unless otherwise noted.

On this page, you can make your own clubs that haven't appeared in the Numberblocks series. You can edit this page to put your fanmade club in it's correct category, or you can just post it in the comments, but you must read the rules before making your club.

Rules

1. Unless specified otherwise, $n \in \N$.
2. Your club must be math-related, and thus must have a formula (with some exceptions, e.g. digit-based patterns). For example, a club for Numberblocks that appeared in 100+ episodes isn't allowed, neither a club for gaming-related Numberblocks, or a club that just focuses on Numberblocks that only appear in 1-2 episodes during the series.
3. The club must not be redundant; for instance, an "Isosceles Triangle" Club is basically just the Square Club (squares can make up-and-down steps, or isosceles triangles). However, you can extend a club's meaning- as long as it's not too redundant.
4. Your club can't just be an obvious mishmash (or in set language, "union") of canon clubs, so you can't have, say, "Step Square Club", which is only for Step Squad and Square Club members. You can't either have something like "Elite Club Member", which just consists of Numberblocks that are in more than 10 clubs.
5. Clubs that aren't defined clearly may be removed.

Linear Pattern Clubs

Linear pattern clubs can be written as $an+b$, where $a$ and $b$ are real constants.

"T" Shape Club

(by NumberVectors)

This club is for numbers that can make a "T" shape. Members include: 5, 8, 11, 14, 17, etc.

The formula is $2n+3$.

Square Fours

(by XhanLu) This club is for any number that are divisible by 4. Members include: 4, 8, 12, 16, 20, 24, 28, 32, 36 etc.

The formula is $4n$.

Cross Club

(by Lookiecookie0505)

The "Cross" Club is for numbers who can make a cross shape; or put simply, making a 2D shape where four one-block wide rods of equal length extend from a single block. Some members were seen in More To Explore. All members of this club are odd. Members of this club include 5, 9, 13, 17, 21, 25 and 29.

The formula is $4n+1$.

High Five Club

(by Eating Crocodiles All The Time)

Numbers multiplied by 5 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 5, 10, 15, 20, 25, 30, 35, 40, 45 and 50, 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.

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

(by Lookiecookie0505)

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 $5n+3$.

Octahedral Club

(by Lookiecookie0505)

The Octahedral Club is for numbers who can make a centered octahedral 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 and 31.

The formula is $6n+1$.

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 $10n$.

Wireframe Club

(by MrYokaiAndWatch902)

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 $12n+8$.

Square with 4 Holes Club

(by XhanLu) The "Square with 4 Holes" (aka Window) club is for numbers where they can make a square with only the frame and the middle rows, forming a window shape. members include: 21, 33, 45, 57, 69, 81, 93, 105, 117, 129 etc.

The formula is $(2(n+1)+1)^2-4n^2$, or $12n+9$.

Quadratic Pattern Clubs

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

Right Triangle Club

(by MrYokaiAndWatch902)

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.

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

Chippy Square Club

(by MrYokaiAndWatch902)

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 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 $n^2+1$.

Frail Cube Club

(by Mr. Yokai)

The "Frail 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.

Circle Club

(by TheMainGus)

If you can make a circle (actually more like squares with blocks attached to the perimeter, or squares without corners). Squares are afraid of circles. One can't get in this club but Five, Twelve, Twenty-One, and Thirty-Two can.

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

TSRITW decided to build upon this idea, because he realized that this club's formula can be rewritten as ${(n+2)^2}-4$. If he ever writes an episode revolving around this club, he would have it be renamed to "Squares Without Corners" Club.

Diamond Club

(by MrYokaiAndWatch902)

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!

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 $2n^2-2n+1$.

Waffle Club

(by Lookiecookie0505)

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, and 96.

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

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 $3n^2-3n+1$.

Cubic Pattern Clubs

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

Ball Club

(by MrYokaiAndWatch902)

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

(by Lookiecookie0505)

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 $7n^3+12n^2+6n+1$.

Higher Power Clubs

Higher power 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.

Hypercube Club

(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 $n^4$.

Exponential Clubs

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

Two-Of-Them Club / Doubler Club

(by Dariber, and Dark Shadow King had a similar idea)

The "Two-Of-Them" 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, 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.

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 $n\geq 0$.

Multi-Variable Clubs

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

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 $c\in\N$.

Rectangle With a Hole In Club

(by Oofy Blox

The "Rectangle With a Hole In" Club is a club for numbers that can make a rectangle with a hole in. Members include Ten, Twelve, Fourteen, Sixteen, Eighteen and Twenty.

Numbers in this club can be written as $2x+2y$, where $x>1$, $y>1$, and $x,y \in \mathbb{N}$.

3-Smooth Club

(by Dozenalism)

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

(by MrYokaiAndWatch902)

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 $a,b \geq 0$ and $a, b \in \Z$.

Times Table-Included Club

(by Lookiecookie0505)

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 $a*b$, 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.

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.

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".)

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

(by MrYokaiAndWatch902)

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

His proof.

(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

(by MrYokaiAndWatch902)

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.

"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

(by TSRITW)

The "Bunny" Club is for the Fibonacci numbers (they originated from a riddle about the population of rabbits). The owner of this club is 34.

The formulas are

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

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

(by TSRITW)

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

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

Prime-Related Clubs

Prime-related clubs are... clubs related to primes. What else did you expect?

Mersenne Club

(by Dozenalism)

Mersenne Primes ONLY! You may join if you're a prime that is one less than a doubler. ($2^n-1$). 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!)

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)

Array Clubs

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

Loop-the-Looper Rectangles Club

(by ButterBlaziken230, 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)

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.

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 that are multiples of Ell. 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.

Numberling-Specific Clubs

Clubs where the members' Numberlings are significant.

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 leads the Palindrome Pals; 22 and 55 are the next highest figured-out members.

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)

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.

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.

Decimal Point Clubs

(by MrYokaiAndWatch902)

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.

Repeating Decimal Club

(by MrYokaiAndWatch902)

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, $0.\overline{142857}$.

Other Clubs

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

Negative Club

(by MrYokaiAndWatch902)

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 $n\in\mathbb{Z}$.

"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.