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 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. 1
 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, 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, 4, 4, 5, 6, 6, 8, 4, 9, 4, 6, 4, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..600 EXAMPLE a(6) = 1 since q(6+0*1/2) + 1 = q(6) + 1 = 5 is prime. a(20) = 1 since q(20+8*9/2) + 1 = q(56) + 1 = 7109 is prime. a(104) = 1 since q(104+15*16/2 + 1 = q(224) + 1 = 1997357057 is prime. a(219) = 1 since q(219+65*66/2) + 1 = q(2364) + 1 = 111369933847869807268722580000364711 is prime. a(1417) > 0 since q(1417+1347*1348/2) + 1 = q(909295) + 1 is prime. MATHEMATICA q[n_]:=PartitionsQ[n] a[n_]:=Sum[If[PrimeQ[q[n+k(k+1)/2]+1], 1, 0], {k, 0, n-1}] Table[a[n], {n, 1, 80}] CROSSREFS Cf. A000009, A000040, A000217, A185636, A239232. Sequence in context: A202495 A103431 A238576 * A125928 A114388 A075789 Adjacent sequences:  A239235 A239236 A239237 * A239239 A239240 A239241 KEYWORD nonn AUTHOR Zhi-Wei Sun, Mar 13 2014 STATUS approved

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Last modified July 4 12:18 EDT 2020. Contains 335448 sequences. (Running on oeis4.)