#prime-numbers — Public Fediverse posts

Now 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 #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

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

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

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

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 #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

A005279: Numbers having divisors d, e with d < e < 2*d
A005279 ➡️ https://oeis.org/A005279

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A005279.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A005279.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A005279.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

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 #php #graph #3D #threejs #webGL #numbers #TwinPrimes #twin #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

A005278: Noncototients: numbers k such that x - phi(x) = k has no solution
A005278 ➡️ https://oeis.org/A005278

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

A005277: Nontotients: even numbers k such that phi(m) = k has no solution.
A005277 ➡️ https://oeis.org/A005277

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

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 #natural #numbers #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieveOfEratosthenes #Eratosthenes #sieve #fundamental #theorem #arithmetic #research

A005244: A self-generating sequence: start with 2 and 3, take all products of any 2 previous elements, subtract 1 and adjoin them to the sequence
A005244 ➡️ https://oeis.org/A005244

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A005244.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A005244.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A005244.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

A005236: Barriers for omega(n): numbers n such that, for all m < n, m + omega(m) <= n
A005236 ➡️ https://oeis.org/A005236

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A005236.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A005236.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A005236.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

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

A005228: Sequence and first differences (A030124) together list all positive numbers exactly once
A005228 ➡️ https://oeis.org/A005228

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A005228.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A005228.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A005228.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

A005214: Triangular numbers together with squares (excluding 0)
A005214 ➡️ https://oeis.org/A005214

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A005214.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A005214.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A005214.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

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 #php #graph #3D #threejs #webGL #numbers #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

A005153: Practical numbers: positive integers m such that every k <= sigma(m) is a sum of distinct divisors of m. Also called panarithmic numbers
A005153 ➡️ https://oeis.org/A005153

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

A005117: Squarefree numbers: numbers that are not divisible by a square greater than 1
A005117 ➡️ https://oeis.org/A005117

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

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 #GIF #graph #3D #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

A005114: Untouchable numbers, also called nonaliquot numbers: impossible values for the sum of aliquot parts function (A001065)
A005114 ➡️ https://oeis.org/A005114

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

A005101: Abundant numbers (sum of divisors of m exceeds 2m)
A005101 ➡️ https://oeis.org/A005101

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

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 #php #graph #3D #threejs #webGL #numbers #primes #PrimeNumbers #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

A005100: Deficient numbers: numbers k such that sigma(k) < 2k
A005100 ➡️ https://oeis.org/A005100

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

A005098: Numbers k such that 4k + 1 is prime
A005098 ➡️ https://oeis.org/A005098

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A005098.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A005098.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A005098.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

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 #Downloads #Algorithms #PARIGP #numbers #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

A004780: Binary expansion contains 2 adjacent 1's
A004780 ➡️ https://oeis.org/A004780

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A004780.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A004780.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A004780.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

A004745: Numbers whose binary expansion does not contain 001
A004745 ➡️ https://oeis.org/A004745

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A004745.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A004745.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A004745.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

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 #php #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

A004743: Numbers whose binary expansion does not contain 110
A004743 ➡️ https://oeis.org/A004743

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A004743.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A004743.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A004743.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

A004614: Numbers that are divisible only by primes congruent to 3 mod 4
A004614 ➡️ https://oeis.org/A004614

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A004614.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A004614.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A004614.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