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

3D graph, threejs - webGL https://decompwlj.com/3Dgraph/A009177.html
3D graph Gen, threejs animation https://decompwlj.com/3DgraphGen/A009177.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/A009177.html

My first, favorite and most important sequence, the weights of prime numbers: A117078
We see prime numbers classified by level and by weight on the graph.

A117078: a(n) is the smallest k such that prime(n+1) = prime(n) + (prime(n) mod k), or 0 if no such k exists https://oeis.org/A117078

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

3D graph, threejs - webGL https://decompwlj.com/3Dgraph/A009112.html
3D graph Gen, threejs animation https://decompwlj.com/3DgraphGen/A009112.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/A009112.html

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
3D graph Gen, threejs animation https://decompwlj.com/3DgraphGen/A008917.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/A008917.html

My data have not been verified but my work is highly reproducible.
- Downloads (csv, img, dump) https://decompwlj.com/
- Algorithms https://oeis.org/wiki/Decomposition_into_weight_*_level_%2B_jump#Algorithms

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

3D graph, threejs - webGL https://decompwlj.com/3Dgraph/A008864.html
3D graph Gen, threejs animation https://decompwlj.com/3DgraphGen/A008864.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/A008864.html

Friends Don't Let Friends Make Bad Graphs! Do you agree with the examples of bad graphs and the alternatives Chenxin Li (@chenxinli2.bsky.social) lists at https://github.com/cxli233/FriendsDontLetFriends #RStats #graphs #dataviz #help

Generation of four sequences decomposed into weight × level + jump (log(weight), log(level), log(jump)) - three.js animation:

1: The natural numbers (A000027) https://decompwlj.com/3DgraphGen/Natural_numbers.html

A008851: Congruent to 0 or 1 mod 5

3D graph, threejs - webGL https://decompwlj.com/3Dgraph/A008851.html
3D graph Gen, threejs animation https://decompwlj.com/3DgraphGen/A008851.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/A008851.html

Decomposition into weight × level + jump of prime numbers:
- a new classification of primes https://decompwlj.com/primedecomp.php
- in 3D - threejs - webGL https://decompwlj.com/3Dgraph/Prime_numbers.html

A008846: Hypotenuses of primitive Pythagorean triangles

3D graph, threejs - webGL https://decompwlj.com/3Dgraph/A008846.html
3D graph Gen, threejs animation https://decompwlj.com/3DgraphGen/A008846.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/A008846.html

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

3D graph, threejs - webGL https://decompwlj.com/3Dgraph/A008810.html
3D graph Gen, threejs animation https://decompwlj.com/3DgraphGen/A008810.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/A008810.html

A008366: 17-rough numbers: smallest prime factor is >= 17

3D graph, threejs - webGL https://decompwlj.com/3Dgraph/A008366.html
3D graph Gen, threejs animation https://decompwlj.com/3DgraphGen/A008366.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/A008366.html

150 sequences decomposed into weight × level + jump in one GIF (log(weight),log(level)):
1000 sequences decomposed on https://decompwlj.com

A008365: 13-rough numbers: positive integers that have no prime factors less than 13

3D graph, threejs - webGL https://decompwlj.com/3Dgraph/A008365.html
3D graph Gen, threejs animation https://decompwlj.com/3DgraphGen/A008365.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/A008365.html

Decomposition into weight × level + jump of prime numbers in 3D, threejs - webGL (log(weight), log(level), log(jump))
https://decompwlj.com/3Dgraph/Prime_numbers.html

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

3D graph, threejs - webGL https://decompwlj.com/3Dgraph/11-rough_numbers.html
3D graph Gen, threejs animation https://decompwlj.com/3DgraphGen/11-rough_numbers.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/11-rough_numbers.html

A007957: Numbers that contain an odd digit

3D graph, threejs - webGL https://decompwlj.com/3Dgraph/A007957.html
3D graph Gen, threejs animation https://decompwlj.com/3DgraphGen/A007957.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/A007957.html

My first, favorite and most important sequence, the weights of prime numbers: A117078
We see prime numbers classified by level and by weight on the graph.

A117078: a(n) is the smallest k such that prime(n+1) = prime(n) + (prime(n) mod k), or 0 if no such k exists https://oeis.org/A117078

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

3D graph, threejs - webGL https://decompwlj.com/3Dgraph/A007932.html
3D graph Gen, threejs animation https://decompwlj.com/3DgraphGen/A007932.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/A007932.html