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A099267: Numbers generated by the golden sieve

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A099267.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A099267.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A099267.html

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Decomposition into weight × level + jump of A099267 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A099267 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

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A099204: A variation on Flavius's sieve (A000960): Start with the natural numbers; at the k-th sieving step, remove every p-th term of the sequence remaining after the (k-1)-st sieving step, where p is the k-th prime; iterate

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A099204.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A099204.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A099204.html

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Decomposition into weight × level + jump of A099204 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A099204 in 2D (log(weight), log(level))

A098058: Prime(n) such that 4 does not divide the difference between prime(n) and prime(n+1)

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A098058.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A098058.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A098058.html

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Decomposition into weight × level + jump of A098058 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A098058 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

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A097933: Primes p that divide 3^((p-1)/2) - 1

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A097933.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A097933.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A097933.html

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Decomposition into weight × level + jump of A097933 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A097933 in 2D (log(weight), log(level))

A097752: Least integer with each "mod 4 prime signature"

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A097752.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A097752.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A097752.html

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Decomposition into weight × level + jump of A097752 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A097752 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

A097102: Numbers m that are the hypotenuse of exactly 13 distinct integer-sided right triangles, i.e., m^2 can be written as a sum of two squares in 13 ways

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A097102.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A097102.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A097102.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 A097102 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A097102 in 2D (log(weight), log(level))

A096777: a(n) = a(n-1) + Sum_{k=1..n-1}(a(k) mod 2), a(1) = 1

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A096777.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A096777.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A096777.html

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Decomposition into weight × level + jump of A096777 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A096777 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

A096526: Initial values for f(x)=phi(sigma(x)) such that iteration of f ends in a cycle of length 4

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A096526.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A096526.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A096526.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 A096526 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A096526 in 2D (log(weight), log(level))

A096246: Base-2 deletable primes (written in base 10)

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A096246.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A096246.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A096246.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 A096246 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A096246 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))

A095954: Initial values for f(x)=phi(sigma(x)) such that iteration of f ends in a cycle of length 6

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A095954.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A095954.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A095954.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 A095954 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A095954 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.

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