OFFSET
1,6
LINKS
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
KEYWORD
nonn
AUTHOR
Ben Branman, Jan 09 2013
STATUS
approved