# #OEIS

One day, one decomposition

A013916: Numbers k such that the sum of the first k primes is prime

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A013916.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A013916.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #sum #first #primes #primenumbers #graph

One day, one decomposition

A011775: Numbers k such that k divides phi(k) * sigma(k)

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A011775.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A011775.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #divides #phi #sigma #graph

One day, one decomposition

A011540: Numbers that contain a 0

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A011540.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A011540.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #contain #digit #graph

One day, one decomposition

A011539: "9ish numbers": decimal representation contains at least one nine

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A011539.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A011539.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #contain #digit #graph

One day, one decomposition

A011533: Numbers that contain a 3

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A011533.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A011533.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #contain #digit #graph

One day, one decomposition

A011532: Numbers that contain a 2

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A011532.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A011532.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #contain #digit #graph

One day, one decomposition

A011531: Numbers that contain a 1

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A011531.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A011531.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #contain #digit #graph

One day, one decomposition

A011257: Geometric mean of phi(n) and sigma(n) is an integer

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A011257.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A011257.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #phi #sigma #graph

One day, one decomposition

A010784: Numbers with distinct decimal digits

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A010784.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A010784.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #distinct #decimal #digits #graph

50 sequences decomposed into weight × level + jump in one GIF

1000 sequences decomposed with 3D graphs (threejs webGL), 2D graphs - CSV, dump, img to download

⬇️⬇️

https://decompwlj.com

#decompwlj ➡️ https://oeis.org/wiki/Decomposition_into_weight_*_level_%2B_jump

#Math #Mathematics #OEIS #sequences #primes #PrimeNumbers #classification #arithmetic #NumberTheory #JavaScript #GIF #graphs

One day, one decomposition

A010064: Base 4 self or Colombian numbers (not of form n + sum of base 4 digits of n)

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A010064.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A010064.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #numbers #3D #sum #base #digits #graph

My first, favorite and most important sequence, the weights of prime numbers

⬇️

http://oeis.org/A117078

We see prime numbers classified by level and by weight on the graph.

This sequence has led to the decomposition into weight × level + jump ➡️ https://oeis.org/wiki/Decomposition_into_weight_*_level_%2B_jump

#decompwlj #math #sequences #OEIS #PrimeNumbers #classification #mathematics #primes #numbers #graph #decomposition #Numbertheory

One day, one decomposition

A010061: Binary self or Colombian numbers: numbers that cannot be expressed as the sum of distinct terms of the form 2^k+1 (k>=0), or equivalently, numbers not of form m + sum of binary digits of m

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/Binary_self_numbers.html

2D #graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/Binary_self_numbers.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #sum #binary #digits #graph

One day, one decomposition

A009177: #Numbers that are the hypotenuses of more than one Pythagorean triangle

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A009177.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A009177.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #hypotenuses #Pythagorean #triangle #graph

One day, one decomposition

A009112: Areas of Pythagorean triangles: numbers which can be the area of a right-angled triangle with integer sides

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A009112.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A009112.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #area #Pythagorean #triangles #graph

150 sequences decomposed into weight × level + jump in one GIF

1000 sequences decomposed with 3D graphs (threejs webGL), 2D graphs - CSV, dump, img to download

⬇️⬇️

https://decompwlj.com

#decompwlj ➡️ https://oeis.org/wiki/Decomposition_into_weight_*_level_%2B_jump

#Math #Mathematics #OEIS #sequences #primes #PrimeNumbers #classification #arithmetic #NumberTheory #JavaScript #GIF #graphs

One day, one decomposition

A008917: Numbers that are the sum of 3 positive cubes in more than one way

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A008917.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A008917.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #sum #cubes #graph

One day, one decomposition

A008864: a(n) = prime(n) + 1

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A008864.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A008864.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #prime #primenumbers #graph

One day, one decomposition

A008851: Congruent to 0 or 1 mod 5

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A008851.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A008851.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #congruent #modulo #graph

One day, one decomposition

A008846: Hypotenuses of primitive Pythagorean triangles

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A008846.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A008846.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #triangles #graph

One day, one decomposition

A008810: a(n) = ceiling(n^2/3)

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A008810.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A008810.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #ceiling #graph

My first, favorite and most important sequence, the weights of prime numbers

⬇️

http://oeis.org/A117078

We see prime numbers classified by level and by weight on the graph.

This sequence has led to the decomposition into weight × level + jump ➡️ https://oeis.org/wiki/Decomposition_into_weight_*_level_%2B_jump

#decompwlj #math #sequences #OEIS #PrimeNumbers #classification #mathematics #primes #numbers #graph #decomposition #Numbertheory

One day, one decomposition

A008366: Smallest prime factor is >= 17

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A008366.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A008366.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #rough #numbers #divisible #graph

One day, one decomposition

A008365: Smallest prime factor is >= 13

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A008365.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A008365.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #rough #numbers #divisible #prime #factor #graph

One day, one decomposition

A008364: 11-rough numbers: not divisible by 2, 3, 5 or 7

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/11-rough_numbers.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/11-rough_numbers.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #rough #numbers #divisible #graph

One day, one decomposition

A007957: Numbers that contain an odd digit

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A007957.html

2D #graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A007957.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #contain #odd #digit #graph

#OEIS A352178

On computing sets of integers with maximum number of pairs summing to powers of 2.

Max A. Alekseyev https://arxiv.org/abs/2303.02872

Originated in April 2021 with Dan Ullman's and Stan Wagon's "Problem of the Week 1321".

It was noted that the problem has a natural interpretation as finding a maximal graph of order n, where the vertices are labeled with pairwise distinct integers and the sum of the endpoint labels for each edge is a power of 2.

Numberphile Youtube https://youtu.be/IPoh5C9CcI8

One day, one decomposition

A007932: Numbers that contain only 1's, 2's and 3's

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A007932.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A007932.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #contain #only #digits #graph

One day, one decomposition

A007921: Numbers that are not the difference of two primes

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A007921.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A007921.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #difference #primes #primenumbers #graph

One day, one decomposition

A007811: Numbers n for which 10n+1, 10n+3, 10n+7 and 10n+9 are primes

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A007811.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A007811.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #primes #primenumbers #form #graph

One day, one decomposition

A007770: Happy numbers: numbers whose trajectory under iteration of sum of squares of digits map (see A003132) includes 1

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/Happy_numbers.html

2D #graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/Happy_numbers.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #trajectory #iteration #sum #squares #digits #map #graph

50 sequences decomposed into weight × level + jump in one GIF

1000 sequences decomposed with 3D graphs (threejs webGL), 2D graphs - CSV, dump, img to download

⬇️⬇️

https://decompwlj.com

#decompwlj ➡️ https://oeis.org/wiki/Decomposition_into_weight_*_level_%2B_jump

#Math #Mathematics #OEIS #sequences #primes #PrimeNumbers #classification #arithmetic #NumberTheory #JavaScript #GIF #graphs

One day, one decomposition

A007703: Regular primes

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/Regular_primes.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/Regular_primes.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #Bernoulli #numbers #divisible #primes #primenumbers #graph

My first, favorite and most important sequence, the weights of prime numbers

⬇️

http://oeis.org/A117078

We see prime numbers classified by level and by weight on the graph.

This sequence has led to the decomposition into weight × level + jump ➡️ https://oeis.org/wiki/Decomposition_into_weight_*_level_%2B_jump

#decompwlj #math #sequences #OEIS #PrimeNumbers #classification #mathematics #primes #numbers #graph #decomposition

One day, one decomposition

A007700: Numbers n such that n, 2n+1, and 4n+3 all prime

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A007700.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A007700.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #primes #primenumbers #graph

One day, one decomposition

A007692: Numbers that are the sum of 2 nonzero squares in 2 or more ways

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A007692.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A007692.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #sum #squares #ways #graph

One day, one decomposition

A007618: a(n) = a(n-1) + sum of digits of a(n-1), a(1) = 5

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A007618.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A007618.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #sum #digits #graph

#OEIS A360923

The Integer Lunar Lander

A position in the game of Integer Lunar Lander consists of an ordered pair (i, j) of integers. There are always 3 legal moves, to (i+1, i+j+1), (i, i+j), and (i-1, i-j-1). The object of the game is to reach (0, 0) in the minimum possible number of moves T(i, j).

The ordered pair may be interpreted as the upward velocity and altitude of a vehicle; the object is to land the vehicle at zero velocity.

Rémy Sigrist's scatterplot:

https://oeis.org/A360923/a360923_1.png

One day, one decomposition

A007606: Take 1, skip 2, take 3, etc

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A007606.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A007606.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #take #skip #graph

One day, one decomposition

A007532: Powerful numbers (2): a sum of positive powers of its digits

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A007532.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A007532.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #powerful #numbers #sum #powers #digits #graph

Do you want to sell the OEIS?

No problem. The OEIS has changed its license to CC-BY-SA-4.0.

The license requires attribution when parts of the OEIS are reproduced.

The new license allows commercial use provided that the result is distributed under the same conditions ("share-alike").

Here's an integer sequence I came up with that I think could be a decent #LullabySequence.

Not in the #OEIS yet - I've got a queue of three to submit now, I think!

2,4,1,5,9,13,17,12,7,2,8,...

As usual: your best guesses for the next terms and the underlying rule, under a content warning, please!

One day, one decomposition

A007066: a(n) = 1 + ceiling((n-1)*phi^2), phi = (1+sqrt(5))/2

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A007066.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A007066.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #ceiling #phi #sqrt #graph

50 sequences decomposed into weight × level + jump in one GIF

⬇️⬇️

https://decompwlj.com

#decompwlj ➡️ https://oeis.org/wiki/Decomposition_into_weight_*_level_%2B_jump

⬇️

http://oeis.org/A117078

We see prime numbers classified by level and by weight on the graph.

#decompwlj #math #sequences #OEIS #PrimeNumbers #classification #mathematics #primes #numbers #graph #decomposition

One day, one decomposition

A006532: Numbers whose sum of divisors is a square

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A006532.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A006532.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #sum #divisors #square #graph

Die fabelhafte Welt der Mathematik: Auf der Suche nach der langweiligsten Zahl der Welt

#Zahlentheorie #FabelhafteMathematik #Zahlen #Sloane #OEIS #Primzahlen #Mathematik

OEIS Foundation Seeks to Raise $3M Endowment to Fund Full-Time Managing Editor

The OEIS style sheet says:

"Avoid vanity: do not name a sequence after yourself (or your family members, your friends, etc.)."

What bad luck! Now that I've found primes I'd like to call 'Peter Primes' (if only for the sake of alliteration.)

So I called them 'primitive prime powers'. They start:

5, 17, 37, 97, 149, ...

But maybe that's for the best, because I have no proof that they're really prime numbers.

If you can prove it, secure eternal glory and enter it in A360204!

A weekend of numbers: Saturday I was number 46 in the LA Tourist race, Sunday I was number 32 in the Coaster Brake Challenge, Monday I was juror number 62 in LA county superior court, so I went to #OEIS to see what number I am today. 41 apparently

(4/4)

The generalized telephone numbers.

Urszula Bednarz and Małgorzata Wołowiec-Musiał, On a new generalization of telephone numbers.

(Python)

from math import factorial, comb

def oddfactorial(n: int) -> int:

return factorial(2 * n) // (2**n * factorial(n))

def T(n: int, k: int) -> int:

return sum(comb(n, 2 * j) * oddfactorial(j) * k**j for j in range(n + 1))

for n in range(10): print([T(n, k) for k in range(8)])

k = 1 gives the standard telefon numbers.

(3/4)

In graph theory, the n-th telephone number is the total number of matchings of a complete graph K_n.

Assuming a telephone system with k possibilities of connections and n subscribers leads to a network that can be modeled by a complete multigraph K(n, k). The total number of connection patterns in such a network is given by A359762.

(2/4)

There are a variety of formulas for the calculation of the telephone numbers.

In the OEIS you can find three different Sage implementations, one more beautiful than the other.

def A(n): return (i/sqrt(2))^n*hermite(n, -i/sqrt(2))

def B(n): return hypergeometric([-n/2, (1-n)/2], [], 2).simplify()

def C(n): return sum(factorial(n) // (factorial(n-2*k) * 2**k * factorial(k)) for k in range(1+n//2))

for f in [A, B, C]: print([f(n) for n in range(20)])

(1/4)

The number of involutions of permutations on n letters, is also known as 'telephone numbers'. According to Bednarz et al. the telephone number interpretation "is due to John Riordan, who noticed that T(n) is the number of connection patterns in a telephone system with n subscribers."

Plot from Wikipedia, Author David Eppstein.

https://en.wikipedia.org/wiki/Telephone_number_(mathematics)

@kimreece there's an entry in the #OEIS giving the end of this process for each starting number: http://oeis.org/A239448

Impressive!

"For people who care about computing the billionth Fibonacci number ..."

Has the existence already been asserted? :fibonacci: 😂

And here is the challenge for the common man (Julia speaking):

function fibrec(n::Int)

n == 0 && return (BigInt(0), BigInt(1))

a, b = fibrec(div(n, 2))

c = a * (b * 2 - a)

d = a * a + b * b

iseven(n) ? (c, d) : (d, c + d)

end

fibonacci(n::Int) = fibrec(n)[1]

println([fibonacci(n) for n in 0:40])

A new sequence of Don Knuth.

Number of fillomino dissections of a 2 X n rectangle.

A fillomino dissection of a rectangle is a tiling by polyominoes in which no two polyominoes of the same size are adjacent.

What a nice coincidence! Neil Sloane uploaded a paper to the arXiv today. The abstract says:

"Someone coming across the sequence 1, 2, 4, 9, 21, 51, 127, . would have had no way (before 1973) of discovering that it had been studied since 1870 (today these are called the Motzkin numbers, and form entry A001006 in the database)."

And I published an entry today on the Motzkin triangle, a refinement of the Motzkin numbers.

The history of a fantastic resource #OEIS https://arxiv.org/pdf/2301.03149.pdf

@hrefna I implemented #LocationLabels using #UlamSpirals, for which I used the #OEIS to find an algorithm to iterate over the spiral (implemented at whenwhere.cf)

I've come up with an integer sequence that doesn't seem to be in the #OEIS yet. Here are the first few terms:

1,2,2,4,3,6,7,8,4,10

Can you work out the rule? I can reveal more terms on request, under a content warning. If you have an idea, please CW it so other people can choose not to see hints

One day, one decomposition

A004780: Binary expansion contains 2 adjacent 1's

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A004780.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A004780.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #number #binary #expansion #contain #adjacent #graph

One day, one decomposition

A004744: Numbers n such that binary expansion does not contain 011

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A004744.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A004744.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #binary #expansion #contain #graph

Came up with another #LullabySequence while getting the toddler to sleep:

1,2,4,3,6,5,10,9,8,7,14,...

This one's already in the #OEIS, so you can spoil yourself if you can't see the pattern

#OEIS A359413

Knuth considered sorting permutations by passing them through a stack. Variations include allowing multiple passes through the stack and using different data structures.

A. Claesson & B. Á. Guðmundsson use pop-stacks in their paper

https://arxiv.org/abs/1710.04978

They show that the generating functions for perms. sortable by k passes are rational for any k. You can find the first six g.f.s on GitHub:

https://github.com/SuprDewd/popstacks

There is also a nice Python program in the OEIS entry.

#OEIS A001181 and A359363.

A Baxter permutation (BP) on {1,2,...,n} is a permutation p = (p1 p2 ... pn) for which there are no quadruples of indices

i < j < j + 1 < k such that

pj < pk < pi < p(j+1) or p(j+1) < pi < pk < pj.

In other words, BPs avoid certain permutation patterns: 2-41-3 and 3-14-2.

There are 1-1 correspondences between BPs and interesting combinatorial objects like floorplan partitions.

This year Don Knuth's Christmas Lecture was about BPs.

https://www.youtube.com/watch?v=zg6YRqT4Duo

I got a nudge to donate to the #OEIS before the year-end, and you know because, I knew I couldn't just donate a round dollar amount, so I donated $0111.21 in honor of A000001. Here's your nudge. Find a sequence and move the decimal place to somewhere you feel comfortable. https://oeisf.org/donate/

I came up with an integer sequence that isn't in the #OEIS, but it's silly:

1,2,2,3,3,4,4,4,4,5,5,5,5,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8, …

Can you give the next 57 terms?

One day, one decomposition

A004214: Positive numbers that are not the sum of three nonzero squares

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A004214.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A004214.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #sum #three #squares #graph

I use #oeis a lot when working through problem sets for #SICP. I feel like it's not cheating though because that last part of coming up with the general formula for describing an integer sequence seems orthogonal to actually getting the sequence itself? I mean I'm doing the experiments and getting the numbers myself?

idk maybe i'm wrong ?

Mark the points of the Farey series F_n on a strip of paper and wrap it around a circle of circumference 1 so the endpoints 0 and 1 coincide; draw a chord between every pair of the Farey points; a(n) is the number of vertices in the resulting graph.

⬇️

http://oeis.org/A117078

We see prime numbers classified by level and by weight on the graph.

#decompwlj #math #sequences #OEIS #PrimeNumbers #classification #mathematics #primes #numbers #graph #decomposition

One day, one decomposition

A003628: Primes congruent to {5, 7} mod 8

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A003628.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A003628.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #primes #PrimeNumbers #congruent #graph

A Beatty sequence is the sequence of integers obtained by taking the floor of the positive multiples of a positive irrational number.

A Cloitre walk is a certain algorithm to visualize a binary sequence.

Sela Fried, in 'The Beauty of Beatty sequences', gives a gallery of 100 of his favorite Cloitre walks.

Plus Python code to generate Cloitre walks of the Beatty sequences B(sqrt(n)).

Download from https://oeis.org/A083035

⬇️

http://oeis.org/A117078

We see prime numbers classified by level and by weight on the graph.

almost done with chapter 1. I have to admit for the exercises I often use #oeis often as an assistant - just because I can't be damned to figure out what the sequences are.

50 sequences decomposed into weight × level + jump in one GIF

1000 sequences decomposed with 3D graph (#threejs #webGL), 2D graphs - CSV, dump, img to download

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https://decompwlj.com

#decompwlj #Math #Mathematics #OEIS #sequences #primes #PrimeNumbers #classification #arithmetic #NumberTheory #JavaScript #GIF #graphs

Mentioned in passing in an old blog post I am finally reading (Playful Math Education, Blog Carnival #157 at http://mathmamawrites.blogspot.com/2022/07/math-teachers-at-play-aka-playful-math.html) is the observation that 157 is the 37th prime, and 37 is also prime.

Now 37 is the 12th prime, and 12 is not prime. That makes me sad but intrigued.

What is the longest chain of prime numbers of this sort? That is "N1 is the N2th prime, and N2 is the N3rd prime, and N3 is the N4th prime…" and so on?

⬇️

http://oeis.org/A117078

We see prime numbers classified by level and by weight on the graph.

I spent the day yesterday writing my first ever R package!!! :blobcatheartbongo: It's installable from GitHub (with a PAT) at the moment, but is missing a lot of functions. :blobcat_glitch:

This package is in support of a paper I am writing which should result in more integer sequences being added to the OEIS (A357257, A357248, and A357266 are already approved), related to my work on intransitivity in paired comparisons :fediverse:

I still haven't solved the mystery of why I have a worksheet working on this problem. But I did find visit the base 10 primes in the #OEIS A085823 and it links this paper posted on the arχiv https://arxiv.org/abs/1912.08598 and that paper links a couple math stackexchange questions, which might explain it a little. But this answer explains the stripes https://math.stackexchange.com/a/3247061/416418 "the length [a substring prime base b] is at most 2𝑝−1 where 𝑝 is the smallest prime that does not divide b"

After a couple tries, I found this sequence of #primenumber counts on #OEIS (you have to include the single digit primes) http://oeis.org/A309572

The OEIS has table of the first 2500 entries and a log scale plot which I recreated here in Maple. The submitter, Rémy Sigrist, identified the pattern based on residues mod 6. Sadly there is no additional work linked.

I've added more colors for b ≡ 0 (mod 30 and 210) and it DOES look like the size depends on the distinct number of primes factors

I have a new #OEIS sequence: " a(n) is the smallest k such that k! has at least n consecutive zeros immediately after the leading digit in base 10."

http://oeis.org/A356739

In case you were wondering, 153 is the smallest integer whose factorial has two zeros after the leading digit. It fits in a toot:

153! = 200634390509568239477828874698911718566246149616161171934231099284840946025238092339613294062603588435530393145048663047173051913507711632216305667129554900620296603188543122491838966881134795135997316305640071571629943041039657861120000000000000000000000000000000000000

This has generated a *superb* integer sequence which isn't yet in the OEIS

@xpil Hello xpil,

thanks for your interesting problem.

I thougt about the knight moves in 3D and made

a model with #GeoGebra: https://www.geogebra.org/3d/awb3hzph

There are 48 moves that lead to 24 fields.

The sequences/functions you mentioned are on #OEIS

http://oeis.org/A024023 and http://oeis.org/A033996

Greetings!