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

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A052405: Numbers without 3 as a digit

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A052405.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A052405.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A052405.html

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Decomposition into weight × level + jump of A052405 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A052405 in 2D (log(weight), log(level))

A052383: Numbers without 1 as a digit

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A052383.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A052383.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A052383.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 A052383 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A052383 in 2D (log(weight), log(level))

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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Decomposition into weight × level + jump of natural numbers: the fundamental theorem of arithmetic and the sieve of Eratosthenes

Graph in 2D (log(weight), log(level)) of the decomposition into weight × level + jump of natural numbers

Decomposition into weight × level + jump of prime numbers: in 2D with sequences on the OEIS: a new classification of primes

Graph in 2D (log(weight), log(level)) of the decomposition into weight × level + jump of prime numbers

A052382: Numbers without 0 in the decimal expansion, colloquial 'zeroless numbers'

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/Zeroless_numbers.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/Zeroless_numbers.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/Zeroless_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 zeroless numbers in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of zeroless numbers in 2D (log(weight), log(level))

A052291: Primes p such that 4p^2 + 1 is also prime

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A052291.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A052291.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A052291.html

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Decomposition into weight × level + jump of A052291 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A052291 in 2D (log(weight), log(level))

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

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Algorithm of the decomposition into weight × level + jump in PARI/GP from the OEIS Wiki

A052223: Numbers whose sum of digits is 9

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A052223.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A052223.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A052223.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 A052223 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A052223 in 2D (log(weight), log(level))

A052214: Numbers n with prime signature(n) = prime signature(n+1) = prime signature(n+2)

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A052214.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A052214.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A052214.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 A052214 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A052214 in 2D (log(weight), log(level))

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

Screenshot of A117078 on the OEIS: https://oeis.org/A117078

Graphs (pin plot and logarithmic scatterplot) of A117078 on the OEIS: https://oeis.org/A117078/graph

A052042: Primes that lack the digit zero in the decimal expansion of their squares

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A052042.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A052042.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A052042.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 A052042 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A052042 in 2D (log(weight), log(level))

A052040: Numbers whose square is zeroless

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A052040.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A052040.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A052040.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 A052040 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A052040 in 2D (log(weight), log(level))

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

A052034: Primes such that the sum of the squares of their digits is also a prime

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A052034.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A052034.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A052034.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 A052034 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A052034 in 2D (log(weight), log(level))

A052033: Primes base 10 that are never primes in any smaller base b, 2<=b<10, expansions interpreted as decimal numbers

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A052033.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A052033.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A052033.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 A052033 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A052033 in 2D (log(weight), log(level))

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 #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 (log(weight), log(level), log(jump)) - threejs - webGL

A052032: Primes base 10 that remain prime in one (and only one) other base b, 2<=b<10, expansions interpreted as decimal numbers

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A052032.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A052032.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A052032.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 A052032 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A052032 in 2D (log(weight), log(level))

Now this animation is available for the 1000 sequences decomposed on my website.
Accessible from the 3Dgraph, 2Dgraph500terms and 2dgraphs pages ➡️ https://decompwlj.com
A little more work on axis sizing and controls.

#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