A003623: Wythoff AB-numbers: floor(floor(n*phi^2)*phi), where phi = (1+sqrt(5))/2

3D graph, threejs - webGL https://decompwlj.com/3Dgraph/A003623.html
3D graph Gen, threejs animation https://decompwlj.com/3DgraphGen/A003623.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/A003623.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

A003601: Numbers j such that the average of the divisors of j is an integer: sigma_0(j) divides sigma_1(j). Alternatively, numbers j such that tau(j) (A000005(j)) divides sigma(j) (A000203(j))

3D graph, threejs - webGL https://decompwlj.com/3Dgraph/A003601.html
3D graph Gen, threejs animation https://decompwlj.com/3DgraphGen/A003601.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/A003601.html

A003512: A Beatty sequence: floor(n*(sqrt(3) + 2))

3D graph, threejs - webGL https://decompwlj.com/3Dgraph/A003512.html
3D graph Gen, threejs animation https://decompwlj.com/3DgraphGen/A003512.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/A003512.html

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

A003511: A Beatty sequence: floor( n * (1 + sqrt(3))/2 )

3D graph, threejs - webGL https://decompwlj.com/3Dgraph/A003511.html
3D graph Gen, threejs animation https://decompwlj.com/3DgraphGen/A003511.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/A003511.html

A003485: Hurwitz-Radon function at powers of 2

3D graph, threejs - webGL https://decompwlj.com/3Dgraph/A003485.html
3D graph Gen, threejs animation https://decompwlj.com/3DgraphGen/A003485.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/A003485.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

A003309: Ludic numbers: apply the same sieve as Eratosthenes, but cross off every k-th remaining number

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

A003277: Cyclic numbers: k such that k and phi(k) are relatively prime; also k such that there is just one group of order k, i.e., A000001(k) = 1

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

A003136: Loeschian numbers: numbers of the form x^2 + xy + y^2; norms of vectors in A2 lattice

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

My second article on Pica this year, this article is about the (big) numbers found in the Pica fonts on typewriters. Featuring my meticulous research[*] and an Italian beauty. Typewriter nerds and font nerds are gonna love it:

https://home.octetfont.com/blog/pica-number.html

[*] a few days and several books and websites.

A003052: Self numbers or Colombian numbers (numbers that are not of the form m + sum of digits of m for any m)

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

A003038: Dimensions of split simple Lie algebras over any field of characteristic zero

3D graph, threejs - webGL https://decompwlj.com/3Dgraph/A003038.html
3D graph Gen, threejs animation https://decompwlj.com/3DgraphGen/A003038.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/A003038.html

A002977: Klarner-Rado sequence: a(1) = 1; subsequent terms are defined by the rule that if m is present so are 2m+1 and 3m+1

3D graph, threejs - webGL https://decompwlj.com/3Dgraph/A002977.html
3D graph Gen, threejs animation https://decompwlj.com/3DgraphGen/A002977.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/A002977.html

A002858: Ulam numbers: a(1) = 1; a(2) = 2; for n>2, a(n) = least number > a(n-1) which is a unique sum of two distinct earlier terms

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

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

Our Numbers Quiz is now live!
How many can you guess right?
https://youknowwhatblog.com/quizzes/numbers-quiz/
.
#pubquiz #pubtrivia #quiz #trivia #triviaquestions #fact #facts #didyouknow #youknowwhat #hard #hardmode #challenge #math #numbers #integer #mathematics #science