A342139 Number of partitions of [2n] into pairs whose sums or differences are primes.

1, 1, 3, 8, 28, 167, 810, 4664, 38344, 207255, 2059900, 19385131, 174417011, 1922011637, 21058799803, 208257199434, 2905150193223, 38462668421772, 481607876817202, 7526871509864950

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Wikipedia, Partition of a set

Example

a(2) = 3: {{1,4}, {2,3}}, {{1,3}, {2,4}}, {{1,2}, {3,4}}.

Maple

b:= proc(s) option remember; `if`(s={}, 1, (j-> add(`if`(i<j and
      ormap(isprime, [j+i, j-i]), b(s minus {i, j}), 0), i=s))(max(s)))
    end:
a:= n-> 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 && AnyTrue[{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 *)

Crossrefs

Cf. A000341, A009692, A342136, A342155.

Sequence in context: A000239 A268302 A345177 * A195687 A060707 A080874

Adjacent sequences: A342136 A342137 A342138 * A342140 A342141 A342142

Keyword

nonn,more

Author

Alois P. Heinz, Mar 01 2021

Status

approved