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

Author

Ben Branman, Jan 09 2013

Keywords

• nonn

Examples

			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.
		

Links

• Eric Weisstein's World of Mathematics, Prime Partition.

Crossrefs

Cf. A000040, A000041, A000607

Programs

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}]