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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

LINKS

Zhi-Wei 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], 2013-2014.

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[n-k]], 1, 0], {k, 1, n-1}]

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

Zhi-Wei Sun, Nov 25 2013

STATUS

approved

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Last modified August 2 20:38 EDT 2021. Contains 346428 sequences. (Running on oeis4.)