A321805 Number of permutations f of {1,...,n} such that k!*f(k) + 1 is prime for every k from 1 to n.

1, 2, 4, 6, 10, 10, 13, 40, 212, 702, 3531, 19008, 34858, 39764, 102312, 47927, 94860, 232006, 658766, 829583, 1547703, 2040211, 32073218, 51347260, 496226762, 1504307318, 16663026685, 125080784519, 241032642271, 1216752358950, 2147004248698, 9320087810948, 19383919945950, 16259146126113, 81023699301023, 124167501991213

Offset

1,2

Comments

Though the first 27 terms are positive, we have a(50) = 0 since all the numbers 50!*k + 1, with k = 1..50, are composite.

Links

Table of n, a(n) for n=1..36.

Example

a(2) = 2 since (1,2) and (2,1) are permutations of {1,2} with 1!*1 + 1 = 2, 2!*2 + 1 = 5, 1!*2 + 1 = 3 and 2!*1 + 1 = 3 all prime.

Mathematica

a[n_]:=a[n]=Permanent[Table[Boole[PrimeQ[i!*j+1]], {i, 1, n}, {j, 1, n}]]; Do[Print[n, " ", a[n]], {n, 1, 27}]

Prog

(PARI) a(n)={matpermanent(matrix(n, n, i, j, isprime(i!*j+1)))} \\ Andrew Howroyd, Nov 19 2018

Crossrefs

Cf. A000040, A000142, A231516, A231631, A321597, A321610, A321611, A321727, A321855.

Sequence in context: A100426 A213474 A187333 * A333412 A089227 A204660

Adjacent sequences: A321802 A321803 A321804 * A321806 A321807 A321808

Keyword

nonn,more

Author

Zhi-Wei Sun, Nov 19 2018

Extensions

a(28)-a(31) from Jinyuan Wang, Jun 13 2020

a(32)-a(36) from Vaclav Kotesovec, Aug 19 2021

Status

approved