A232186 - OEIS

A232186

Number of ways to write n = p + q (q > 0) with p and p^3 + n*q^2 both prime.

0, 0, 1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 2, 2, 3, 2, 2, 5, 1, 1, 3, 1, 5, 4, 2, 3, 3, 1, 2, 3, 2, 4, 6, 2, 3, 5, 2, 3, 3, 3, 2, 3, 4, 2, 4, 3, 2, 2, 3, 2, 6, 2, 3, 3, 5, 4, 4, 4, 5, 9, 1, 4, 7, 3, 4, 6, 3, 5, 8, 3, 5, 6, 5, 5, 13, 2, 4, 5, 4, 4, 7, 5, 5, 13, 3, 5, 8, 6, 4, 6, 4, 3, 8, 3, 4, 9, 1, 4, 11, 3

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OFFSET

1,5

COMMENTS

Conjecture: a(n) > 0 for all n > 2.

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Zhi-Wei Sun, Conjectures involving primes and quadratic forms, preprint, arXiv:1211.1588.

EXAMPLE

a(10) = 1 since 10 = 7 + 3 with 7 and 7^3 + 10*3^2 = 433 both prime.

a(11) = 1 since 11 = 5 + 6 with 5 and 5^3 + 11*6^2 = 521 both prime.

a(124) = 1 since 124 = 19 + 105 with 19 and 19^3 + 124*105^2 = 1373959 both prime.