#sieve — Public Fediverse posts

"decompwlj 3D" by Opus 5: interactive app of 3D graphs with three.js ➡️ https://decompwlj.com/decompwlj3dopus/ ⬅️

#decompwlj #math #AI #Opus5 #app #3D #threejs #sequence #numbers #sieve

A073121: a(n) = r*a(ceiling(n/2)) + s*a(floor(n/2)) with a(1)=1 and (r,s)=(2,2)
A073121 ➡️ https://oeis.org/A073121

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A073121.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A073121.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A073121.html

#decompwlj #math #numbers #sequence #threejs #3D #graph #sieve

A073120: Areas of Pythagorean (or right) triangles with integer sides of the form (2mn, m^2 - n^2, m^2 + n^2)
A073120 ➡️ https://oeis.org/A073120

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A073120.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A073120.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A073120.html

#decompwlj #math #numbers #sequence #threejs #3D #graph #sieve

A072978: Numbers of the form m * 2^bigomega(m), where m>1 is odd and bigomega(m) = A001222(m), the number of prime factors of m
A072978 ➡️ https://oeis.org/A072978

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A072978.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A072978.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A072978.html

#decompwlj #math #numbers #sequence #threejs #3D #graph #sieve

A072859: Primes p for which the period of 1/p is prime
A072859 ➡️ https://oeis.org/A072859

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A072859.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A072859.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A072859.html

#decompwlj #math #numbers #sequence #threejs #3D #graph #sieve

Opus 5 - High-res PNG (slight offset from the origin):
The triangular numbers are all level-classified

#decompwlj #math #graph #AI #Claude #triangular #numbers #sieve

Opus 5 - High-res PNG (slight offset from the origin):
All 5,761,452 decomposable primes < 10^8

#decompwlj #math #graph #AI #Claude #prime #numbers #sieve

Opus 5 - High-res PNG (slight offset from the origin):
The base case: the natural numbers - the weight sheet is the sieve of Eratosthenes

#decompwlj #math #graph #AI #Claude #natural #numbers #sieve

A072774: Powers of squarefree numbers
A072774 ➡️ https://oeis.org/A072774

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A072774.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A072774.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A072774.html

#decompwlj #math #numbers #sequence #threejs #3D #graph #sieve

A072587: Numbers having at least one prime factor with an even exponent
A072587 ➡️ https://oeis.org/A072587

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A072587.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A072587.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A072587.html

#decompwlj #math #numbers #sequence #threejs #3D #graph #sieve

Opus 5 - High-res PNG (slight offset from the origin):
The base-10 palindromes - a plate that repeats itself every two digits

#decompwlj #math #graph #AI #Anthropic #Claude #Opus #Opus5 #mathematics #sequence #base #numbers #NumberTheory #sieve #arithmetic #classification #decomposition

Opus 5 - High-res PNG (slight offset from the origin):
The triangular numbers are all level-classified

#decompwlj #math #graph #AI #Anthropic #Claude #Opus #Opus5 #mathematics #sequence #triangular #numbers #TriangularNumbers #NumberTheory #sieve #arithmetic #classification #decomposition

Opus 5 - High-res PNG (slight offset from the origin):
The base case: the natural numbers - the weight sheet is the sieve of Eratosthenes

#decompwlj #math #graph #AI #Anthropic #Claude #Opus #Opus5 #mathematics #sequence #natural #numbers #NaturalNumbers #sieveOfEratosthenes #NumberTheory #sieve #arithmetic #classification #decomposition

Opus 5 - High-res PNG (slight offset from the origin):
All 5,761,452 decomposable primes < 10^8

#decompwlj #math #graph #AI #Anthropic #Claude #Opus #Opus5 #mathematics #sequence #numbers #prime #PrimeNumbers #NumberTheory #sieve #arithmetic #classification #decomposition

Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ https://decompwlj.com/Opus5_decompwlj_pedagogical_treatise_9th_edition_2026_08_16.html

The weight is unique:
"The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."

Proof of Conjecture 9:
"This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."

The atlas as an instrument:
"About a thousand OEIS sequences have been decomposed and published at https://decompwlj.com. Today that is an archive. It could be an instrument."

#decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition

A072502: Numbers that are run sums (trapezoidal, the difference between two triangular numbers) in exactly 3 ways
A072502 ➡️ https://oeis.org/A072502

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A072502.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A072502.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A072502.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

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

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

A072437: Numbers with no prime factors of form 4*k+3
A072437 ➡️ https://oeis.org/A072437

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A072437.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A072437.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A072437.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ https://decompwlj.com/Opus5_decompwlj_pedagogical_treatise_9th_edition_2026_08_16.html

The weight is unique:
"The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."

Proof of Conjecture 9:
"This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."

The atlas as an instrument:
"About a thousand OEIS sequences have been decomposed and published at https://decompwlj.com. Today that is an archive. It could be an instrument."

#decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition

A072225: Numbers k such that prime(k) + prime(k+1) + prime(k+2) is prime
A072225 ➡️ https://oeis.org/A072225

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A072225.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A072225.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A072225.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

In the decomposition into weight × level + jump, the Twin Prime Conjecture becomes: "The number of prime numbers with a weight of 3 is infinite"

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #graph #3D #threejs #webGL #numbers #TwinPrimes #twin #primes #conjecture #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

A072202: Same numbers of prime factors of forms 4*k+1 and 4*k+3, counted with multiplicity
A072202 ➡️ https://oeis.org/A072202

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A072202.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A072202.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A072202.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ https://decompwlj.com/Opus5_decompwlj_pedagogical_treatise_9th_edition_2026_08_16.html

The weight is unique:
"The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."

Proof of Conjecture 9:
"This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."

The atlas as an instrument:
"About a thousand OEIS sequences have been decomposed and published at https://decompwlj.com. Today that is an archive. It could be an instrument."

#decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition

A072140: The period length of the 'Reverse and Subtract' trajectory of n is greater than 1
A072140 ➡️ https://oeis.org/A072140

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A072140.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A072140.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A072140.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

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 #numbers #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #SieveofEratosthenes #sieve #Eratosthenes #fundamental #theorem #arithmetic #research

A072055: a(n) = 2*prime(n)+1
A072055 ➡️ https://oeis.org/A072055

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A072055.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A072055.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A072055.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ https://decompwlj.com/Opus5_decompwlj_pedagogical_treatise_9th_edition_2026_08_16.html

The weight is unique:
"The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."

Proof of Conjecture 9:
"This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."

The atlas as an instrument:
"About a thousand OEIS sequences have been decomposed and published at https://decompwlj.com. Today that is an archive. It could be an instrument."

#decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition

A071403: Which squarefree number is prime? a(n)-th squarefree number equals n-th prime
A071403 ➡️ https://oeis.org/A071403

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A071403.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A071403.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A071403.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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

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 #3D #numbers #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

A071395: Primitive abundant numbers (abundant numbers all of whose proper divisors are deficient numbers)
A071395 ➡️ https://oeis.org/A071395

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A071395.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A071395.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A071395.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #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