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

1,1

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

Zhi-Wei 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

Zhi-Wei Sun, Jan 24 2014

Status

approved