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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

%I

%S 1,2,3,4,6,17,24,37,44,95,121,162,165,247,263,601,714,742,762,804,

%T 1062,1144,1149,1323,1508,1755,1833,1877,2330,2380,2599,3313,3334,

%U 3368,3376,3395,3504,3688,3881,4294,4598,4611,5604,5696,5764,5988,6552,7206,7540,7689

%N 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).

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

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

%C See also A236440 for a similar sequence.

%H Zhi-Wei Sun, <a href="/A236413/b236413.txt">Table of n, a(n) for n = 1..200</a>

%H Z.-W. Sun, <a href="http://arxiv.org/abs/1402.6641">Problems on combinatorial properties of primes</a>, arXiv:1402.6641, 2014

%e a(1) = 1 since p(1)^2 + q(1)^2 = 1^2 + 1^2 = 2 is prime.

%e a(2) = 2 since p(2)^2 + q(2)^2 = 2^2 + 1^2 = 5 is prime.

%e a(3) = 3 since p(3)^2 + q(3)^2 = 3^2 + 2^2 = 13 is prime.

%t pq[n_]:=PrimeQ[PartitionsP[n]^2+PartitionsQ[n]^2]

%t n=0;Do[If[pq[m],n=n+1;Print[n," ",m]],{m,1,10000}]

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

%K nonn

%O 1,2

%A _Zhi-Wei Sun_, Jan 24 2014

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Last modified August 24 16:10 EDT 2019. Contains 326295 sequences. (Running on oeis4.)