Lmst

A056874: Primes of form x^2+xy+3y^2, discriminant -11

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A056874.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A056874.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A056874.html

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Decomposition into weight × level + jump of A056874 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A056874 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

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A056868: Numbers that are not nilpotent numbers

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A056868.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A056868.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A056868.html

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Decomposition into weight × level + jump of A056868 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A056868 in 2D (log(weight), log(level))

A056867: Nilpotent numbers: n such that every group of order n is nilpotent

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

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

Decomposition into weight × level + jump of nilpotent numbers 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

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

Decomposition into weight × level + jump of prime numbers in 3D (log(weight), log(level), log(jump)) - threejs - webGL

A056866: Orders of non-solvable groups, i.e., numbers that are not solvable numbers

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A056866.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A056866.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A056866.html

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Decomposition into weight × level + jump of A056866 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A056866 in 2D (log(weight), log(level))

A056815: Primes with prime "look and say" descriptions

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A056815.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A056815.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A056815.html

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Decomposition into weight × level + jump of A056815 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A056815 in 2D (log(weight), log(level))

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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A056809: Numbers k such that k, k+1 and k+2 are products of two primes

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A056809.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A056809.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A056809.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 A056809 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A056809 in 2D (log(weight), log(level))

A056709: Naught-y primes, primes with noughts (or zeros)

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

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

Decomposition into weight × level + jump of naught-y primes 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

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

A056524: Palindromes with even number of digits

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A056524.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A056524.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A056524.html

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Decomposition into weight × level + jump of A056524 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A056524 in 2D (log(weight), log(level))

A056020: Numbers that are congruent to +-1 mod 9

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A056020.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A056020.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A056020.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 A056020 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A056020 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

A055638: Numbers k for which sigma(k^2) is prime

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A055638.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A055638.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A055638.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 A055638 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A055638 in 2D (log(weight), log(level))

A055393: Sum of a square and a nonnegative cube in more than one way

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A055393.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A055393.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A055393.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 A055393 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A055393 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

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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

A055039: Numbers of the form 2^(2i+1)*(8j+7)

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A055039.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A055039.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A055039.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 A055039 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A055039 in 2D (log(weight), log(level))

Picking the Right Chart Library (Without the Headache) https://orendra.com/blog/picking-the-right-chart-library-without-the-headache/ #opensource #graphs #apexcharts #char.js #rechart

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.

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#graphs

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