A093437 a(n) = largest prime of the form n!/k! + 1.

2, 2, 3, 7, 13, 61, 31, 2521, 20161, 15121, 604801, 39916801, 3991681, 3113510401, 14529715201, 54486432001, 10461394944001, 59281238016001, 53353114214401, 2, 670442572801, 8515157028618240001, 9366672731480064001

Offset: 0

Author

Amarnath Murthy, Apr 01 2004

Keywords

• nonn

Comments

Is 19 the largest n such that a(n) = 2? There are none for 19 < n <= 600. - Robert Israel, Jan 16 2017

Examples

			a(7) = 2521 because 7!/2! + 1 = 2521 is prime, whereas 7!/1! + 1 = 5041 = 71^2 is composite;
a(19) = 2 because the only prime of the form 19!/k! + 1 is 19!/19! + 1 = 2.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..466

Crossrefs

Cf. A093621 (smallest k > 0 such that n!/k! + 1 is prime), A002981 (n! + 1 is prime), A088332 (primes of form n! + 1).

Programs

Maple

f:= proc(n) local k,x;
  x:= n!;
  for k from 2 do
    if isprime(x+1) then return x+1 fi;
    x:= x/k;
  od
end proc:
map(f, [$0..40]); # Robert Israel, Jan 16 2017

Mathematica

a[n_] := Module[{k, x}, x = n!; For[k = 2, True, k++, If[PrimeQ[x+1], Return[x+1]]; x = x/k]];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Feb 08 2023, after Robert Israel *)

Extensions

Corrected and extended by Hugo Pfoertner, Apr 06 2004