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A052018: Numbers k with the property that the sum of the digits of k is a substring of k

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A052018.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A052018.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A052018.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 A052018 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A052018 in 2D (log(weight), log(level))

A051936: Truncated triangular numbers: a(n) = n*(n+1)/2 - 9

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

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

Decomposition into weight × level + jump of truncated triangular numbers in 2D (log(weight), log(level))

A051795: Doubly balanced primes: primes which are averages of both their immediate and their second neighbors

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

Decomposition into weight × level + jump of doubly balanced primes in 2D (log(weight), log(level))

A051750: Primes whose cubes lack zeros

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A051750.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A051750.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A051750.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 A051750 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A051750 in 2D (log(weight), log(level))

A051677: Tetrahedron-tree numbers: a(n)=sum(b(m),m=1..n), b(m)=1, 1,3, 1,3,6, 1,3,6,10,..., 1,2,...,i*(i+1)2

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

Decomposition into weight × level + jump of tetrahedron-tree 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 #webGL #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

A051635: Weak primes: prime(n) < (prime(n-1) + prime(n+1))/2

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

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

A051634: Strong primes: prime(k) > (prime(k-1) + prime(k+1))/2

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

Decomposition into weight × level + jump of strong primes 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

A051507: Primes p such that p*q+2 is prime, where q is next prime after p

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A051507.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A051507.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A051507.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 A051507 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A051507 in 2D (log(weight), log(level))

A051283: Numbers k such that if one writes k = Product p_i^e_i (p_i primes) and P = max p_i^e_i, then k/P > P

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A051283.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A051283.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A051283.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 A051283 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A051283 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 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

A051146: Sequence b(n) mentioned in A051145

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A051146.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A051146.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A051146.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 A051146 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A051146 in 2D (log(weight), log(level))

A051004: Numbers divisible both by their individual digits and by the sum of their digits

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A051004.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A051004.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A051004.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 A051004 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A051004 in 2D (log(weight), log(level))

A050936: Sum of two or more consecutive prime numbers

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A050936.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A050936.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A050936.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 A050936 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A050936 in 2D (log(weight), log(level))

Complex plane iteratables

#Fractal #FractalFriday #Complex #Mathematics #Grid #Shadertoy #GLSL #WebGL #CreativeCoding

A distorted 2D grid in black on a bright solid background.

The same grid again, with much more distortion and complex shapes emerging.

$The same "grid" again, now distorted a bunch of times, resulting into tree-like fractal patterns.$

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