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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). 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 17 06:06 EST 2019. Contains 329217 sequences. (Running on oeis4.)