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

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

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

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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

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A049068: Complement of quarter-squares (A002620)

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A049068.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A049068.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A049068.html

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Decomposition into weight × level + jump of A049068 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A049068 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

A049039: Geometric Connell sequence: 1 odd, 2 even, 4 odd, 8 even, ...

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

Decomposition into weight × level + jump of geometric Connell sequence in 2D (log(weight), log(level))

Working through Wacław Sierpiński's /250 Problems in Elementary Number Theory/ (1964 in Polish; 1970 aug. and trans. in English; available on archive.org and in less savory places) to keep my tools sharpened while I get up to speed on algebraic number theory, and I've got to say, these are really, *really* fun problems! ☺️ #numbertheory #math

A048992: Hannah Rollman's numbers: the numbers excluded from A048991

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

Decomposition into weight × level + jump of Hannah Rollman's numbers 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

A048991: Write down the numbers 1,2,3,... but omit any number (such as 12 or 23 or 31 ...) which appears in the concatenation of all earlier terms

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A048991.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A048991.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A048991.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 A048991 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A048991 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))
Decomposition into weight × level + jump of A048991 in 2D (log(weight), log(level))

A048989: Numbers k such that pi(k) is prime

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A048989.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A048989.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A048989.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 A048989 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A048989 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

A048701: List of binary palindromes of even length (written in base 10)

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A048701.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A048701.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A048701.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 A048701 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A048701 in 2D (log(weight), log(level))

A048653: Numbers k such that the decimal digits of k^2 can be partitioned into two or more nonzero squares

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A048653.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A048653.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A048653.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 A048653 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A048653 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