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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).

%I A236414 #6 Jan 25 2014 01:11:52
%S A236414 2,5,13,29,137,89653,2495509,468737369,5654578481,10952004689145437,
%T A236414 4227750418844538601,16877624537532512753869,29718246090638680022401,
%U A236414 33479444420637044862046313837,386681772864767371008755193761
%N 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).
%C A236414 This is a subsequence of A233346. All terms after the first term are congruent to 1 modulo 4.
%C A236414 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.
%H A236414 Zhi-Wei Sun, <a href="/A236414/b236414.txt">Table of n, a(n) for n = 1..50</a>
%e A236414 a(1) = 2 since 2 = p(1)^2 + q(1)^2 is prime.
%t A236414 a[n_]:=PartitionsP[A236413(n)]^2+PartitionsQ[A236413(n)]^2
%t A236414 Table[a[n],{n,1,15}]
%Y A236414 Cf. A000009, A000010, A000040, A000041, A233346, A236412, A236413.
%K A236414 nonn
%O A236414 1,1
%A A236414 _Zhi-Wei Sun_, Jan 24 2014