A093621 -id:A093621 - cp's OEIS frontend

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

Amarnath Murthy, Apr 01 2004

nonn

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

			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.

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

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

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

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 *)

Corrected and extended by Hugo Pfoertner, Apr 06 2004

A093623 Smallest k>0 such that n!/k!-1 is prime.

Original entry on oeis.org

1, 1, 2, 1, 1, 3, 2, 6, 3, 1, 8, 1, 4, 3, 3, 3, 5, 3, 15, 13, 13, 10, 8, 4, 5, 12, 14, 1, 2, 1, 1, 5, 13, 11, 11, 1, 25, 4, 2, 32, 3, 4, 15, 9, 10, 34, 16, 3, 5, 23, 13, 30, 3, 13, 7, 34, 3, 21, 22, 9, 10, 15, 7, 26, 51, 42, 18, 6, 6, 31, 23, 31, 51, 12, 20, 8, 24, 50, 40, 4, 30, 49, 36, 4, 23

Offset: 3

Hugo Pfoertner, Apr 06 2004

nonn

a(A002982(n)) = 1. The existence of a solution has been checked up to n=500.

The results were computed using the PrimeFormGW (PFGW) primality-testing program. - Hugo Pfoertner, Nov 14 2019

			a(10) = 6 because 10!/6! - 1 = 5039 is prime, whereas 10!/k! - 1 is composite for k = 1..5.

Cf. A093622 largest prime of the form n!/k!-1, A002982 n!-1 is prime, A093621 smallest k>0 such that n!/k!+1 is prime.

a(53) corrected by Gionata Neri, Jul 18 2017

cp's OEIS Frontend

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

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