A066953 Integers of the form (k!+1)/prime(k).

1, 1, 11, 104956945995541, 6458007542034006723505363870885661685813595082173513446600259282126155549185667752443

Offset: 1

Author

Benoit Cloitre, Feb 01 2002

Keywords

• nonn
• hard

Comments

The next term has more than 6.5*10^7 digits, if it exists. - Amiram Eldar, Apr 22 2025

Crossrefs

Cf. A068000.

Programs

Mathematica

f[k_] := (k! + 1)/Prime[k]; f /@ Select[Range[100], IntegerQ[f[#]] &] (* Amiram Eldar, Apr 22 2025 *)

PARI

list(lim) = {my(k = 0, r = 1); forprime(p = 1, lim, k++; r *= k; if(!((r+1) % p), print1((r+1)/p, ", ")));} \\ Amiram Eldar, Apr 22 2025

Formula

a(n) = (A068000(n)!+1)/prime(A068000(n)). - Amiram Eldar, Apr 22 2025