A236440 Positive integers m with A000009(m)^2 + A047967(m)^2 prime.

2, 3, 4, 13, 18, 23, 44, 52, 54, 67, 82, 93, 139, 155, 166, 185, 196, 249, 299, 333, 382, 559, 574, 911, 939, 1076, 1077, 1386, 1707, 1710, 1872, 2041, 2120, 2172, 2234, 2810, 3272, 3407, 3442, 3469, 3551, 3657, 3694, 4185, 4282, 4469, 4554, 5273, 5315, 5729

Offset

1,1

Comments

According to the conjecture in A236439, this sequence should have infinitely many terms.

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) = 2 since A000009(2)^2 + A047967(2)^2 = 1^2 + 1^2 =2 is prime, but A000009(1)^2 + A047967(1)^2 = 1^2 + 0^2 is not.

Mathematica

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

Crossrefs

Cf. A000009, A000040, A047967, A236413, A236418, A236439.

Sequence in context: A102947 A281512 A295396 * A357954 A162222 A010346

Adjacent sequences: A236437 A236438 A236439 * A236441 A236442 A236443

Keyword

nonn

Author

Zhi-Wei Sun, Jan 25 2014

Status

approved