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A122094: Prime divisors of Mersenne numbers. Primes p such that the multiplicative order of 2 modulo p is prime
A122094 ➡️ https://oeis.org/A122094

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A122094.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A122094.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A122094.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 A122094 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A122094 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.

#decompwlj #math #mathematics #maths #sequence #OEIS #graph #natural #numbers #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

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

A121943: Numbers k such that the central binomial coefficient C(2k,k) is divisible by k^2
A121943 ➡️ https://oeis.org/A121943

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A121943.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A121943.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A121943.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 A121943 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A121943 in 2D (log(weight), log(level))

A121539: Numbers whose binary expansion ends in an even number of 1's
A121539 ➡️ https://oeis.org/A121539

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A121539.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A121539.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A121539.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 A121539 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A121539 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

A121032: Multiples of 12 containing a 12 in their decimal representation
A121032 ➡️ https://oeis.org/A121032

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A121032.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A121032.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A121032.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 A121032 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A121032 in 2D (log(weight), log(level))

Interesting blog post about text classification using compression, specifically the new "compression.zstd" module contributed by @emmatyping

https://maxhalford.github.io/blog/text-classification-zstd/

#compression #zstd #zstandard #classification

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

A121030: Multiples of 10 containing a 10 in their decimal representation
A121030 ➡️ https://oeis.org/A121030

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A121030.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A121030.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A121030.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 A121030 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A121030 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

A121022: Even numbers containing a 2 in their decimal representation
A121022 ➡️ https://oeis.org/A121022

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A121022.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A121022.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A121022.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 A121022 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A121022 in 2D (log(weight), log(level))

A120944: Composite squarefree numbers
A120944 ➡️ https://oeis.org/A120944

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A120944.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A120944.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A120944.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 A120944 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A120944 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

#decompwlj #math #mathematics #maths #sequence #OEIS #graph #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research #GIF

A119735: Numbers n such that every digit occurs at least once in n^3
A119735 ➡️ https://oeis.org/A119735

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A119735.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A119735.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A119735.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 A119735 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A119735 in 2D (log(weight), log(level))

A119617: Integers of the form c(n)/b(n) where c(n+1)=c(n)+(n+1)^4 with c(0)=1 and b(n+1)=b(n)+(n+1)^2 with b(0)=1
A119617 ➡️ https://oeis.org/A119617

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A119617.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A119617.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A119617.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 A119617 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A119617 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

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