Lmst

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

#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

A057165: Indices of addition steps in Recamán's sequence A005132

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A057165.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A057165.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A057165.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 A057165 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A057165 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

A056875: Generated by sieving the natural numbers: keep the smallest remaining number k and take out its k-th successor l as well as the l-th successor m of l, the m-th successor of m and so on. Then start again from the next remaining number

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A056875.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A056875.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A056875.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 A056875 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A056875 in 2D (log(weight), log(level))

The Representation Theory of Finite Groups by Walter Feit (PDF)
Author: Walter Feit
File Type: PDF
Download at https://sci-books.com/the-representation-theory-of-finite-groups-0444557296/
#Theory, #WalterFeit

Finite-Dimensional Division Algebras over Fields by Nathan Jacobson (PDF)
Author: Nathan Jacobson
File Type: PDF
Download at https://sci-books.com/finite-dimensional-division-algebras-over-fields-3540570292/
#Theory, #NathanJacobson

I'm working on a theory #research #theory

The Unreasonable Effectiveness of Mathematics in the Physical Sciences
— Eugene Wigner, 1959, Communications on Pure and Applied Mathematics. 13 (1): 1–14
https://webhomes.maths.ed.ac.uk/~v1ranick/papers/wigner.pdf

I have just re-read this after too many decades. Treat yourself if you have any interest in maths, physics, beauty, philosophy, or writing. It contains no equations, though it does discuss a small number.

#mathematics #physics #theory #philosophy #knowledge #epistemology #pdf #logic #quantum #relativity

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

#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 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

#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

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

#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 A056868 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

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

Beautiful Abelian Sandpiles

https://eavan.blog/posts/beautiful-sandpiles.html

#HackerNews #Beautiful #Abelian #Sandpiles #mathematics #chaos #theory #combinatorics #sandpile #model

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

#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 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

#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