A324372 Number of permutations p of [n] whose absolute displacements |p(i)-i| are prime numbers.

1, 0, 0, 0, 1, 2, 9, 28, 144, 640, 2348, 6740, 37161, 208186, 1410137, 8322892, 47973920, 231922220, 1747678465, 11712495736, 101585559496, 776251710048, 6154289307912, 41248110305520, 397850617247393

Offset

0,6

Links

Table of n, a(n) for n=0..24.

Wikipedia, Permutation

Example

a(4) = 1: 3412.
a(5) = 2: 34512, 45123.
a(6) = 9: 345621, 351624, 356124, 451623, 456123, 456231, 645123, 645231, 651234.

Maple

b:= proc(s) option remember; (n-> `if`(n=0, 1, add(`if`(
     isprime(abs(n-j)), b(s minus {j}), 0), j=s)))(nops(s))
    end:
a:= n-> b({$1..n}):
seq(a(n), n=0..16);

Mathematica

b[s_] := b[s] = With[{n = Length[s]}, If[n==0, 1, Sum[If[
     PrimeQ[Abs[n-j]], b[s ~Complement~ {j}], 0], {j, s}]]];
a[n_] := b[Range[n]];
a /@ Range[0, 16] (* Jean-François Alcover, Mar 25 2021, after Alois P. Heinz *)

Crossrefs

Cf. A000040, A000142, A324373, A324374, A324375, A324376.

Sequence in context: A086511 A291632 A328281 * A138912 A374827 A002747

Adjacent sequences: A324369 A324370 A324371 * A324373 A324374 A324375

Keyword

nonn

Author

Alois P. Heinz, Feb 25 2019

Status

approved