

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).


3



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

1,1


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.


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..50


EXAMPLE

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


MATHEMATICA

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


CROSSREFS

Cf. A000009, A000010, A000040, A000041, A233346, A236412, A236413.
Sequence in context: A178444 A299145 A122025 * A057873 A116699 A290198
Adjacent sequences: A236411 A236412 A236413 * A236415 A236416 A236417


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Jan 24 2014


STATUS

approved



