A236414 Primes of the form p(m)^2 + q(m)^2 with m > 0, where p(.) is the partition function (A000041) and q(.) is the strict partition function (A000009).

2, 5, 13, 29, 137, 89653, 2495509, 468737369, 5654578481, 10952004689145437, 4227750418844538601, 16877624537532512753869, 29718246090638680022401, 33479444420637044862046313837, 386681772864767371008755193761

Offset: 1

Author

Zhi-Wei Sun, Jan 24 2014

Keywords

• nonn

Comments

This is a subsequence of A233346. All terms after the first term are congruent to 1 modulo 4.

According to the conjecture in A236412, this sequence should have infinitely many terms. See A236413 for positive integers m with p(m)^2 + q(m)^2 prime.

Examples

			a(1) = 2 since 2 = p(1)^2 + q(1)^2 is prime.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A000009, A000010, A000040, A000041, A233346, A236412, A236413.

Programs

Mathematica

a[n_]:=PartitionsP[A236413(n)]^2+PartitionsQ[A236413(n)]^2
Table[a[n],{n,1,15}]