A342136 Number of partitions of [2n] into pairs whose sums and differences are primes.

1, 0, 0, 0, 1, 2, 6, 10, 22, 101, 66, 504, 2088, 3572, 14398, 49984, 108030, 191228, 1087758, 5005440, 14081453, 97492234, 160186634, 939652634, 3926077642, 4273706733, 41832174879, 214185383046, 494248121522, 6153003414039, 38125026176659, 13635112709648, 39350572537836, 511502485322923, 1069875349612147, 5075263842958032

Offset: 0

Author

Alois P. Heinz, Mar 01 2021

Keywords

• nonn

Examples

			a(4) = 1: {{1,6}, {2,5}, {3,8}, {4,7}}.
a(5) = 2: {{1,6}, {2,9}, {3,10}, {4,7}, {5,8}}, {{1,6}, {2,5}, {3,8}, {4,9}, {7,10}}.
		

Links

• Wikipedia, Partition of a set

Crossrefs

Cf. A000341, A009692, A342139, A342155.

Programs

Maple

b:= proc(s) option remember; `if`(s={}, 1, (j-> add(`if`(i b({$1..2*n}):
seq(a(n), n=0..15);

Mathematica

b[s_] := b[s] = If[s == {}, 1, With[{j = Max[s]}, Sum[If[i < j && AllTrue[{j+i, j-i}, PrimeQ], b[s ~Complement~ {i, j}], 0], {i, s}]]];
a[n_] := b[Range[2n]];
a /@ Range[0, 15] (* Jean-François Alcover, Aug 25 2021, after Alois P. Heinz *)

Extensions

a(25)-a(35) from Bert Dobbelaere, Mar 06 2021