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 A071059 Number of ways of pairing even numbers in the range 1 to n with odd numbers in the range n+1 to 2n such that each pair sums to a prime. 2
 1, 1, 1, 1, 1, 2, 2, 6, 4, 7, 6, 11, 11, 53, 53, 181, 171, 939, 925, 4432, 4545, 15811, 15583, 67891, 68193, 434963, 388975, 2718150, 3113343, 21580655, 18425145, 92370364, 94887088, 564878656, 572364768, 4545704064, 4092294083, 36878092180, 36363930614 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 LINKS Martin Fuller, Table of n, a(n) for n = 1..70 FORMULA a(2n) = A071058(2n). EXAMPLE a(6)=2 because there are two ways: 2+9, 4+7, 6+11 and 2+11, 4+9, 6+7. MAPLE f:= proc(n) local m; m:= floor(n/2); LinearAlgebra:-Permanent(Matrix(m, m, (i, j) -> `if`(isprime((i+j-2)*2 + n + 3 + (n mod 2)), 1, 0))) end proc: f(1):= 1: map(f, [\$1..40]); # Robert Israel, Sep 21 2023 MATHEMATICA a[n_] := a[n] = If[n == 1, 1, Module[{s1, s2, s3, s4, i, ik, km}, s1 = Select[Flatten[Outer[List, Range[2, n, 2], Range[2n-1, n+1, -2]], 1], PrimeQ[Total[#]]&]; s2 = SplitBy[s1, First]; km = Length[s2]; ik = Table[{i[k], 1, Length[s2[[k]]]}, {k, 1, km}]; s3 = Table[Table[s2[[k, i[k]]], {k, 1, km}], Evaluate[Sequence @@ ik]] // Flatten[#, km - 1]&; s4 = Select[s3, Length[Union[Flatten[#]]] == 2km&]; s4 // Length]]; Table[Print[n, " ", a[n]]; a[n], {n, 1, 20}] (* Jean-François Alcover, Aug 10 2022 *) PROG (PARI) a(n)=matpermanent(matrix(n\2, n\2, i, j, isprime((i+j-2)*2+n+3+(n%2)))); \\ Martin Fuller, Sep 21 2023 CROSSREFS The product of this sequence and A071058 gives A070897. Sequence in context: A067804 A074911 A174222 * A256468 A061108 A284918 Adjacent sequences: A071056 A071057 A071058 * A071060 A071061 A071062 KEYWORD nice,nonn,changed AUTHOR T. D. Noe, May 25 2002 EXTENSIONS More terms from David W. Wilson, May 27 2002 a(31)-a(37) from Donovan Johnson, Aug 12 2010 STATUS approved

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Last modified September 23 12:40 EDT 2023. Contains 365551 sequences. (Running on oeis4.)