A342155 Number of partitions of [2n] into pairs such that either their sum or their absolute difference is a prime (but not both).

1, 1, 2, 3, 7, 26, 55, 282, 1520, 2685, 27005, 171474, 768123, 5936728, 43976303, 207493790, 2570789335, 21669733984, 136340261314, 1639978185920

Offset: 0

Author

Alois P. Heinz, Mar 02 2021

Keywords

• nonn
• more

Examples

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

Links

• Wikipedia, Partition of a set

Crossrefs

Cf. A000040, A000341, A009692, A291564, A342136, A342139.

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 && (PrimeQ[j + i] ~Xor~ PrimeQ[j - i]), 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 *)