cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A228430 Number of ways to write n = x + y (x, y > 0) with x^4 + y*(y+1)/2 prime.

Original entry on oeis.org

0, 1, 1, 2, 2, 0, 2, 3, 2, 3, 2, 3, 4, 1, 2, 1, 4, 3, 1, 1, 6, 4, 2, 4, 4, 4, 1, 5, 3, 5, 6, 4, 6, 3, 5, 5, 6, 3, 3, 5, 5, 5, 9, 3, 3, 11, 6, 7, 4, 8, 7, 12, 7, 5, 10, 4, 3, 8, 8, 3, 11, 6, 5, 10, 4, 6, 14, 6, 3, 9, 3, 12, 12, 9, 3, 11, 6, 10, 15, 7, 7, 8, 3, 6, 11, 8, 11, 10, 7, 3, 11, 10, 7, 11, 4, 6, 13, 11, 9, 8
Offset: 1

Views

Author

Zhi-Wei Sun, Nov 10 2013

Keywords

Comments

Conjecture: (i) a(n) > 0 except for n = 1, 6.
(ii) For any positive integer n not among 1, 3, 14, 25, there are positive integers x and y with x + y = n such that x^3 + y*(y+1)/2 is prime.

Examples

			a(14) = 1 since 14 = 4 + 10 with 4^4 + 10*11/2 = 311 prime.
a(27) = 1 since 27 = 22 + 5 with 22^4 + 5*6/2 = 234271 prime.
		

Crossrefs

Programs

  • Mathematica
    a[n_]:=Sum[If[PrimeQ[x^4+(n-x)(n-x+1)/2],1,0],{x,1,n-1}]
    Table[a[n],{n,1,100}]