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, 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

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: A353297 A103431 A238576 * A125928 A114388 A075789

Adjacent sequences: A239235 A239236 A239237 * A239239 A239240 A239241

Keyword

nonn

Author

Zhi-Wei Sun, Mar 13 2014

Status

approved