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A324372 Number of permutations p of [n] whose absolute displacements |p(i)-i| are prime numbers. 4
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Mar 25 2021, after Alois P. Heinz *)

CROSSREFS

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

Sequence in context: A086511 A291632 A328281 * A138912 A002747 A110377

Adjacent sequences:  A324369 A324370 A324371 * A324373 A324374 A324375

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 25 2019

STATUS

approved

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Last modified September 30 02:05 EDT 2022. Contains 357095 sequences. (Running on oeis4.)