

A232504


Number of ways to write n = k + m (k, m > 0) with p(k) + q(m) prime, where p(.) is the partition function (A000041) and q(.) is the strict partition function (A000009).


11



0, 1, 2, 2, 1, 1, 4, 1, 5, 4, 5, 4, 4, 3, 5, 5, 6, 2, 4, 8, 4, 3, 6, 5, 3, 5, 5, 8, 5, 6, 4, 7, 5, 5, 2, 6, 9, 8, 3, 10, 7, 9, 7, 4, 7, 8, 8, 5, 6, 8, 5, 4, 8, 5, 5, 7, 11, 7, 7, 9, 8, 7, 9, 11, 8, 10, 4, 7, 8, 7, 9, 13, 7, 8, 4, 6, 11, 8, 13, 3, 8, 10, 5, 7, 11, 11, 6, 9, 6, 5, 10, 6, 9, 5, 10, 11, 9, 8, 11, 8
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OFFSET

1,3


COMMENTS

Conjecture: a(n) > 0 for all n > 1.


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..10000
Z.W. Sun, On a^n+ bn modulo m, arXiv preprint arXiv:1312.1166 [math.NT], 20132014.


EXAMPLE

a(5) = 1 since 5 = 1 + 4 with p(1) + q(4) = 1 + 2 = 3 prime.
a(8) = 1 since 8 = 4 + 4 with p(4) + q(4) = 5 + 2 = 7 prime.


MATHEMATICA

a[n_]:=Sum[If[PrimeQ[PartitionsP[k]+PartitionsQ[nk]], 1, 0], {k, 1, n1}]
Table[a[n], {n, 1, 100}]


CROSSREFS

Cf. A000009, A000040, A000041, A202650, A231201.
Sequence in context: A279104 A165509 A100996 * A292201 A343070 A090048
Adjacent sequences: A232501 A232502 A232503 * A232505 A232506 A232507


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Nov 25 2013


STATUS

approved



