Lmst

A102487: Numbers in base-12 representation that can be written with decimal digits

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A102487.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A102487.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A102487.html

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Decomposition into weight × level + jump of A102487 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A102487 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

A101594: Numbers with exactly two distinct decimal digits, neither of which is 0

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A101594.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A101594.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A101594.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 A101594 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A101594 in 2D (log(weight), log(level))

Yesterday I had to fit an ICCID number (15-22 digits) in a 64 bits wide integer. Not possible, bad specification. This night I thought that a 72 bits integer could be used (there is a spare byte in the memory). That's not fully right : (2^72-1)-(10^22-1) is negative. But at least, it could be usefull for ICCID up to 20 digits.
One condition, find the algorithm to convert a string as char[20] into a table of 9 bytes. Fun.
#digits #integer #C #embeddedSystem

A101082: Numbers n such that binary representation contains bit strings "10" and "01" (possibly overlapping)

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A101082.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A101082.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A101082.html

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Decomposition into weight × level + jump of A101082 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A101082 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

A100959: Non-semiprimes

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A100959.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A100959.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A100959.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 non-semiprimes in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of non-semiprimes 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

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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A100493: a(n) = n + n-th semiprime

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A100493.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A100493.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A100493.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 A100493 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A100493 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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Decomposition into weight × level + jump of A089194 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A089194 in 2D (log(weight), log(level))

A100484: The primes doubled; even semiprimes

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

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

A100201: Primes of the form 23n+3

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A100201.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A100201.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A100201.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 A100201 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A100201 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