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

Author

Zhi-Wei Sun, Jan 25 2014

Keywords

• nonn

Comments

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

Examples

			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.
		

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

Crossrefs

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

Programs

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}]