cp's OEIS Frontend

A239238 a(n) = |{0 <= k < n: q(n+k*(k+1)/2) + 1 is prime}|, where q(.) is the strict partition function given by A000009.

%I A239238 #15 Nov 07 2024 21:58:31
%S A239238 1,2,3,2,3,1,4,5,2,4,5,4,4,4,2,4,3,6,3,1,3,5,5,5,2,9,8,7,5,3,3,4,3,7,
%T A239238 4,8,6,2,6,6,5,2,5,5,3,3,4,4,7,7,8,5,5,4,8,6,3,4,3,5,11,2,2,4,6,6,5,5,
%U A239238 4,4,5,6,6,8,4,9,4,6,4,3
%N A239238 a(n) = |{0 <= k < n: q(n+k*(k+1)/2) + 1 is prime}|, where q(.) is the strict partition function given by A000009.
%C A239238 We note that a(n) > 0 for n up to 3580 with the only exception n = 1831. Also, for n = 722, there is no number k among 0, ..., n with q(n+k*(k+1)/2) - 1 prime.
%H A239238 Zhi-Wei Sun, <a href="/A239238/b239238.txt">Table of n, a(n) for n = 1..600</a>
%e A239238 a(6) = 1 since q(6+0*1/2) + 1 = q(6) + 1 = 5 is prime.
%e A239238 a(20) = 1 since q(20+8*9/2) + 1 = q(56) + 1 = 7109 is prime.
%e A239238 a(104) = 1 since q(104+15*16/2) + 1 = q(224) + 1 = 1997357057 is prime.
%e A239238 a(219) = 1 since q(219+65*66/2) + 1 = q(2364) + 1 = 111369933847869807268722580000364711 is prime.
%e A239238 a(1417) > 0 since q(1417+1347*1348/2) + 1 = q(909295) + 1 is prime.
%t A239238 q[n_]:=PartitionsQ[n]
%t A239238 a[n_]:=Sum[If[PrimeQ[q[n+k(k+1)/2]+1],1,0],{k,0,n-1}]
%t A239238 Table[a[n],{n,1,80}]
%Y A239238 Cf. A000009, A000040, A000217, A185636, A239232.
%K A239238 nonn
%O A239238 1,2
%A A239238 _Zhi-Wei Sun_, Mar 13 2014