cp's OEIS Frontend

A232186 Number of ways to write n = p + q (q > 0) with p and p^3 + n*q^2 both prime.

%I A232186 #7 Nov 20 2013 09:08:43
%S A232186 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,
%T A232186 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,
%U A232186 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
%N A232186 Number of ways to write n = p + q (q > 0) with p and p^3 + n*q^2 both prime.
%C A232186 Conjecture: a(n) > 0 for all n > 2.
%H A232186 Zhi-Wei Sun, <a href="/A232186/b232186.txt">Table of n, a(n) for n = 1..10000</a>
%H A232186 Zhi-Wei Sun, <a href="http://arxiv.org/abs/1211.1588">Conjectures involving primes and quadratic forms</a>, preprint, arXiv:1211.1588.
%e A232186 a(10) = 1 since 10 = 7 + 3 with 7 and 7^3 + 10*3^2 = 433 both prime.
%e A232186 a(11) = 1 since 11 = 5 + 6 with 5 and 5^3 + 11*6^2 = 521 both prime.
%e A232186 a(124) = 1 since 124 = 19 + 105 with 19 and 19^3 + 124*105^2 = 1373959 both prime.
%t A232186 a[n_]:=Sum[If[PrimeQ[Prime[k]^3+n*(n-Prime[k])^2],1,0],{k,1,PrimePi[n-1]}]
%t A232186 Table[a[n],{n,1,100}]
%Y A232186 Cf. A000040, A219864, A220413, A232174.
%K A232186 nonn
%O A232186 1,5
%A A232186 _Zhi-Wei Sun_, Nov 20 2013