#decomposition — Public Fediverse posts

This animation is available for the 1000 sequences decomposed on my website.
Accessible from the 3Dgraph, 2Dgraph500terms and 2dgraphs pages ➡️ https://decompwlj.com

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

This animation is available for the 1000 sequences decomposed on my website.
Accessible from the 3Dgraph, 2Dgraph500terms and 2dgraphs pages ➡️ https://decompwlj.com

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

4: The palindromes in base 10 (A002113) ➡️ https://decompwlj.com/3DgraphGen/Palindromes.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

4: The palindromes in base 10 (A002113) ➡️ https://decompwlj.com/3DgraphGen/Palindromes.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

3: The triangular numbers (A000217) ➡️ https://decompwlj.com/3DgraphGen/Triangular_numbers.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

3: The triangular numbers (A000217) ➡️ https://decompwlj.com/3DgraphGen/Triangular_numbers.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

2: The prime numbers (A000040) ➡️ https://decompwlj.com/3DgraphGen/Prime_numbers.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

2: The prime numbers (A000040) ➡️ https://decompwlj.com/3DgraphGen/Prime_numbers.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

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

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

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

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

A061641: Pure numbers in the Collatz (3x+1) iteration. Also called pure hailstone numbers
A061641 ➡️ https://oeis.org/A061641

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A061641.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A061641.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A061641.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

A061641: Pure numbers in the Collatz (3x+1) iteration. Also called pure hailstone numbers
A061641 ➡️ https://oeis.org/A061641

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A061641.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A061641.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A061641.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

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

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

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

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

A061426: Geometric mean of the digits = 2. In other words, the product of the digits is = 2^k where k is the number of digits
A061426 ➡️ https://oeis.org/A061426

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A061426.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A061426.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A061426.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

A061426: Geometric mean of the digits = 2. In other words, the product of the digits is = 2^k where k is the number of digits
A061426 ➡️ https://oeis.org/A061426

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A061426.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A061426.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A061426.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

A061384: Numbers n such that sum of digits = number of digits
A061384 ➡️ https://oeis.org/A061384

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A061384.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A061384.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A061384.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

A061384: Numbers n such that sum of digits = number of digits
A061384 ➡️ https://oeis.org/A061384

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A061384.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A061384.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A061384.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

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

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

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

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

A061346: Odd numbers that are neither primes nor prime powers
A061346 ➡️ https://oeis.org/A061346

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A061346.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A061346.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A061346.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

A061346: Odd numbers that are neither primes nor prime powers
A061346 ➡️ https://oeis.org/A061346

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A061346.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A061346.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A061346.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

A061276: Numbers that are sums of repdigits of their digits
A061276 ➡️ https://oeis.org/A061276

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A061276.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A061276.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A061276.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

A061276: Numbers that are sums of repdigits of their digits
A061276 ➡️ https://oeis.org/A061276

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A061276.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A061276.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A061276.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

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

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

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

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

A060947: Intrinsic 10-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base
A060947 ➡️ https://oeis.org/A060947

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A060947.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A060947.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A060947.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

A060947: Intrinsic 10-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base
A060947 ➡️ https://oeis.org/A060947

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A060947.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A060947.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A060947.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

A060879: Intrinsic 9-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base
A060879 ➡️ https://oeis.org/A060879

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A060879.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A060879.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A060879.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

A060879: Intrinsic 9-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base
A060879 ➡️ https://oeis.org/A060879

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A060879.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A060879.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A060879.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

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

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

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

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

A060874: Intrinsic 4-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base
A060874 ➡️ https://oeis.org/A060874

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A060874.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A060874.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A060874.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

A060874: Intrinsic 4-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base
A060874 ➡️ https://oeis.org/A060874

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A060874.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A060874.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A060874.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

A059708: Numbers k such that all digits have same parity
A059708 ➡️ https://oeis.org/A059708

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A059708.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A059708.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A059708.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

A059708: Numbers k such that all digits have same parity
A059708 ➡️ https://oeis.org/A059708

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A059708.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A059708.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A059708.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

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

#decompwlj #math #mathematics #maths #sequence #OEIS #PARIGP #Downloads #Algorithms #numbers #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

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

#decompwlj #math #mathematics #maths #sequence #OEIS #PARIGP #Downloads #Algorithms #numbers #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

A059456: Unsafe primes: primes not in A005385
A059456 ➡️ https://oeis.org/A059456

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

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

A059456: Unsafe primes: primes not in A005385
A059456 ➡️ https://oeis.org/A059456

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

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

A059404: Numbers with different exponents in their prime factorizations
A059404 ➡️ https://oeis.org/A059404

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A059404.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A059404.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A059404.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

A059404: Numbers with different exponents in their prime factorizations
A059404 ➡️ https://oeis.org/A059404

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A059404.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A059404.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A059404.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

In the decomposition into weight × level + jump, the Twin Prime Conjecture becomes: "The number of prime numbers with a weight of 3 is infinite"

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

In the decomposition into weight × level + jump, the Twin Prime Conjecture becomes: "The number of prime numbers with a weight of 3 is infinite"

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

A059401: Numbers that contain as proper substrings every maximal prime power dividing them
A059401 ➡️ https://oeis.org/A059401

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A059401.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A059401.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A059401.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

A059401: Numbers that contain as proper substrings every maximal prime power dividing them
A059401 ➡️ https://oeis.org/A059401

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A059401.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A059401.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A059401.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

A059269: Numbers m for which the number of divisors, tau(m), is divisible by 3
A059269 ➡️ https://oeis.org/A059269

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A059269.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A059269.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A059269.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

A059269: Numbers m for which the number of divisors, tau(m), is divisible by 3
A059269 ➡️ https://oeis.org/A059269

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A059269.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A059269.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A059269.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

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.

#decompwlj #math #mathematics #maths #sequence #OEIS #graph #numbers #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #SieveofEratosthenes #sieve #Eratosthenes #fundamental #theorem #arithmetic #research

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.

#decompwlj #math #mathematics #maths #sequence #OEIS #graph #numbers #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #SieveofEratosthenes #sieve #Eratosthenes #fundamental #theorem #arithmetic #research

A058972: For a rational number p/q let f(p/q) = sum of aliquot divisors of p+q divided by number of divisors of p+q; sequence gives numbers k such that, starting at k/1 and iterating f, an integer is eventually reached
A058972 ➡️ https://oeis.org/A058972

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A058972.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A058972.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A058972.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

A058972: For a rational number p/q let f(p/q) = sum of aliquot divisors of p+q divided by number of divisors of p+q; sequence gives numbers k such that, starting at k/1 and iterating f, an integer is eventually reached
A058972 ➡️ https://oeis.org/A058972

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A058972.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A058972.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A058972.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

A058369: Numbers k such that k and k^2 have same digit sum
A058369 ➡️ https://oeis.org/A058369

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A058369.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A058369.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A058369.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

A058369: Numbers k such that k and k^2 have same digit sum
A058369 ➡️ https://oeis.org/A058369

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A058369.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A058369.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A058369.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

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

#decompwlj #math #mathematics #maths #sequence #OEIS #graph #numbers #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

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

#decompwlj #math #mathematics #maths #sequence #OEIS #graph #numbers #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

A057436: Contains digits 1 through 6 only
A057436 ➡️ https://oeis.org/A057436

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A057436.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A057436.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A057436.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

A057436: Contains digits 1 through 6 only
A057436 ➡️ https://oeis.org/A057436

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A057436.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A057436.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A057436.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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