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

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

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We see the fundamental theorem of arithmetic and the sieve of Eratosthenes in the decomposition into weight × level + jump of natural numbers. Applied to prime numbers this decomposition leads to a new classification of primes.

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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))
A003601 ➡️ https://oeis.org/A003601

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

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A003485: Hurwitz-Radon function at powers of 2
A003485 ➡️ https://oeis.org/A003485

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

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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

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A003309: Ludic numbers: apply the same sieve as Eratosthenes, but cross off every k-th remaining number
A003309 ➡️ https://oeis.org/A003309

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

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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
A003277 ➡️ https://oeis.org/A003277

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

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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

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A003136: Loeschian numbers: numbers of the form x^2 + xy + y^2; norms of vectors in A2 lattice
A003136 ➡️ https://oeis.org/A003136

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

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #php #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research