A230091: Numbers of the form k + wt(k) for exactly two distinct k, where wt(k) = A000120(k) is the binary weight of k
A230091 ➡️ https://oeis.org/A230091

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A230091.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A230091.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A230091.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:
- 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

A230044: Numbers k such that k plus a perfect square is a triangular number
A230044 ➡️ https://oeis.org/A230044

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A230044.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A230044.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A230044.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

A228183: Semiprimes generated by the Euler polynomial x^2 + x + 41
A228183 ➡️ https://oeis.org/A228183

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A228183.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A228183.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A228183.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

150 sequences decomposed into weight × level + jump in one GIF (log(weight),log(level)):
1000 sequences decomposed on https://decompwlj.com

#decompwlj #math #mathematics #maths #sequence #OEIS #graph #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research #GIF

A227916: Primes that remain prime when the leftmost digit is removed
A227916 ➡️ https://oeis.org/A227916

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A227916.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A227916.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A227916.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

If, for natural numbers 𝑎,𝑏,𝑛

\[a \times b \equiv 1 \pmod n\]

is it obvious that either
\[a \equiv b \equiv 1 \pmod n\]
or
\[a \equiv b \equiv -1 \pmod n\]

Does this require special justification?

(is it one of those maths results that looks obvious but isn't)

#maths #numbertheory

A217139: Numbers n such that phi(n) = phi(n+12), with Euler's totient function phi = A000010
A217139 ➡️ https://oeis.org/A217139

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A217139.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A217139.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A217139.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 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

A216838: Odd primes for which 2 is not a primitive root
A216838 ➡️ https://oeis.org/A216838

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A216838.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A216838.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A216838.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