The sequence having the greatest known growth rate while remaining fully decomposable under the #decompwlj criterion is A003312
a(1) = 3; for n>0, a(n+1) = a(n) + floor((a(n)-1)/2): https://oeis.org/A003312
Table of n, a(n) for n = 1..1000: https://oeis.org/A003312/b003312.txt

#math #numbers #sequence #OEIS #sieve

A006567: Emirps (primes whose reversal is a different prime)
A006567 ➡️ https://oeis.org/A006567

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

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 #sieveOfEratosthenes #Eratosthenes #sieve #fundamental #theorem #arithmetic #research

A006562: Balanced primes (of order one): primes which are the average of the previous prime and the following prime
A006562 ➡️ https://oeis.org/A006562

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

A006532: Numbers whose sum of divisors is a square
A006532 ➡️ https://oeis.org/A006532

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A006532.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A006532.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A006532.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

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

A006512: Greater of twin primes
A006512 ➡️ https://oeis.org/A006512

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

Here's a sequence that I can sort of believe isn't in the #OEIS, but really should be for completeness:

1,1,3,3,3,6,7,7,9, ...

a(n) is the smallest integer k such that all numbers up to n are in the Collatz trajectory of some number less than or equal to k.

It's an upper bound for a sequence that is in, A372810: the smallest number whose Collatz trajectory contains n.

Can I be bothered to submit it? probs not!

A006463: Convolve natural numbers with characteristic function of triangular numbers
A006463 ➡️ https://oeis.org/A006463

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A006463.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A006463.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A006463.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