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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).
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%I #6 Jan 25 2014 01:11:52

%S 2,5,13,29,137,89653,2495509,468737369,5654578481,10952004689145437,

%T 4227750418844538601,16877624537532512753869,29718246090638680022401,

%U 33479444420637044862046313837,386681772864767371008755193761

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

%C 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 Zhi-Wei Sun, <a href="/A236414/b236414.txt">Table of n, a(n) for n = 1..50</a>

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

%t a[n_]:=PartitionsP[A236413(n)]^2+PartitionsQ[A236413(n)]^2

%t Table[a[n],{n,1,15}]

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

%K nonn

%O 1,1

%A _Zhi-Wei Sun_, Jan 24 2014