%I #6 Jul 04 2015 15:55:21
%S 2,5,13,29,53,229,509,709,1021,1789,3137,3257,3361,6829,13337,18229,
%T 30977,41177,49201,148229,240101,240109,250301,1004053,1575029,
%U 2511601,3833989,3851989,6314389,5934121,9060109,9148309,13823549,20842361,31404937,106714213,116703973,151536109,221241901,254416549
%N Primes of the form p(k)^2 + p(m)^2, where k and m are positive integers, and p(.) is the partition function given by A000041.
%C The conjecture in A259531 implies that the current sequence has infinitely many terms.
%D Zhi-Wei Sun, Problems on combinatorial properties of primes, in: M. Kaneko, S. Kanemitsu and J. Liu (eds.), Number Theory: Plowing and Starring through High Wave Forms, Proc. 7th China-Japan Seminar (Fukuoka, Oct. 28 - Nov. 1, 2013), Ser. Number Theory Appl., Vol. 11, World Sci., Singapore, 2015, pp. 169-187.
%H Zhi-Wei Sun, <a href="/A259678/b259678.txt">Table of n, a(n) for n = 1..10000</a>
%H Zhi-Wei Sun, <a href="http://arxiv.org/abs/1402.6641">Problems on combinatorial properties of primes</a>, arXiv:1402.6641 [math.NT], 2014.
%e a(1) = 2 since p(1)^2 + p(1)^2 = 2 is prime.
%e a(2) = 5 since p(1)^2 + p(2)^2 = 1^2 + 2^2 = 5 is prime.
%e a(3) = 13 since p(2)^2 + p(3)^2 = 2^2 + 3^2 = 13 is prime.
%e a(4) = 29 since p(2)^2 + p(4)^2 = 2^2 + 5^2 = 29 is prime.
%t n=0;Do[If[PrimeQ[PartitionsP[k]^2+PartitionsP[m]^2],n=n+1;Print[n," ",PartitionsP[k]^2+PartitionsP[m]^2]],{m,1,34},{k,1,m}]
%Y Cf. A000040, A000041, A259531.
%K nonn
%O 1,1
%A _Zhi-Wei Sun_, Jul 03 2015
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