A236413 Positive integers m with p(m)^2 + q(m)^2 prime, where p(.) is the partition function (A000041) and q(.) is the strict partition function (A000009).

1, 2, 3, 4, 6, 17, 24, 37, 44, 95, 121, 162, 165, 247, 263, 601, 714, 742, 762, 804, 1062, 1144, 1149, 1323, 1508, 1755, 1833, 1877, 2330, 2380, 2599, 3313, 3334, 3368, 3376, 3395, 3504, 3688, 3881, 4294, 4598, 4611, 5604, 5696, 5764, 5988, 6552, 7206, 7540, 7689

Offset

1,2

Comments

According to the conjecture in A236412, this sequence should have infinitely many terms.

See A236414 for primes of the form p(m)^2 + q(m)^2.

See also A236440 for a similar sequence.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..200

Z.-W. Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014

Example

a(1) = 1 since p(1)^2 + q(1)^2 = 1^2 + 1^2 = 2 is prime.
a(2) = 2 since p(2)^2 + q(2)^2 = 2^2 + 1^2 = 5 is prime.
a(3) = 3 since p(3)^2 + q(3)^2 = 3^2 + 2^2 = 13 is prime.

Mathematica

pq[n_]:=PrimeQ[PartitionsP[n]^2+PartitionsQ[n]^2]
n=0; Do[If[pq[m], n=n+1; Print[n, " ", m]], {m, 1, 10000}]

Crossrefs

Cf. A000009, A000010, A000040, A233346, A236412, A236414, A236417, A236418, A236419, A236440.

Sequence in context: A026094 A285191 A271360 * A069860 A084391 A259383

Adjacent sequences: A236410 A236411 A236412 * A236414 A236415 A236416

Keyword

nonn

Author

Zhi-Wei Sun, Jan 24 2014

Status

approved