A202177 Number of partitions p of n such that each part of p is prime and each part of the conjugate partition of p is also prime.

0, 0, 0, 1, 0, 2, 0, 1, 1, 2, 0, 2, 2, 2, 2, 3, 3, 0, 4, 2, 5, 2, 4, 3, 8, 2, 6, 4, 11, 0, 10, 4, 14, 2, 14, 4, 21, 2, 20, 5, 25, 0, 28, 6, 30, 2, 38, 5, 46, 0, 44, 4, 54, 0, 56, 6, 67, 2, 72, 4, 93, 2, 74, 7, 113, 0, 100, 8, 131, 0, 128

Offset

1,6

Links

Table of n, a(n) for n=1..71.

Eric Weisstein's World of Mathematics, Prime Partition.

Example

For n=17, there are three valid partitions: (7,7,3), its conjugate partition (3,3,3,2,2,2,2), and the self-conjugate partition (5,5,3,2,2).
Thus a(17)=3.

Mathematica

ConjugatePartition[l_List] :=
 Module[{i, r = Reverse[l], n = Length[l]},
  Table[n + 1 - Position[r, _?(# >= i &), Infinity, 1][[1, 1]], {i,
    l[[1]]}]]; f[n_] := Select[Select[IntegerPartitions[n], And @@ (PrimeQ[#]) &],
  And @@ (PrimeQ[ConjugatePartition[#]]) &]; a[n_] := Length[f[n]]; Table[a[n], {n, 1, 40}]

Crossrefs

Cf. A000040, A000041, A000607

Sequence in context: A083715 A037135 A374521 * A354793 A029360 A337541

Adjacent sequences: A202174 A202175 A202176 * A202178 A202179 A202180

Keyword

nonn

Author

Ben Branman, Jan 09 2013

Status

approved