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%I #16 Aug 25 2021 05:27:57
%S 1,1,3,8,28,167,810,4664,38344,207255,2059900,19385131,174417011,
%T 1922011637,21058799803,208257199434,2905150193223,38462668421772,
%U 481607876817202,7526871509864950
%N Number of partitions of [2n] into pairs whose sums or differences are primes.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%e a(2) = 3: {{1,4}, {2,3}}, {{1,3}, {2,4}}, {{1,2}, {3,4}}.
%p b:= proc(s) option remember; `if`(s={}, 1, (j-> add(`if`(i<j and
%p ormap(isprime, [j+i, j-i]), b(s minus {i, j}), 0), i=s))(max(s)))
%p end:
%p a:= n-> b({$1..2*n}):
%p seq(a(n), n=0..15);
%t 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}]]];
%t a[n_] := b[Range[2n]];
%t a /@ Range[0, 15] (* _Jean-François Alcover_, Aug 25 2021, after _Alois P. Heinz_ *)
%Y Cf. A000341, A009692, A342136, A342155.
%K nonn,more
%O 0,3
%A _Alois P. Heinz_, Mar 01 2021
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