A078814 Smallest prime factor of googolplex - n that exceeds 13, or 1 if googolplex - n is 13-smooth.

17, 1433, 499679, 1279, 31, 149

Offset: 1

Author

Ed Pegg Jr and Robert G. Wilson v, Dec 06 2002

Keywords

• nonn
• hard
• more
• fini

Comments

Seventh term is not known. Sequence continues ?, 625392489737, 19, 37, 5419, 107, 23, 60149, 1733, 89, 8543, 17, 5261, 229, 8656871, 4273, 14009, 29, 509, 43628661784403, 24539783, 19, 347, 12414692011, 523, 151, 421, 35816135619181, 17, 23, 184309, ?, 181, 288481, 163, 41, 743, 13337, 71, 53, 19, 59, 113, 37957721, ... where the unknown numbers exceed 25 * 10^12. - Dario Alpern, Jul 03 2003

Links

• Dario Alejandro Alpern, Factors of 1000 numbers up to googolplex.

Crossrefs

Cf. A072288, A200924, A227247.

Programs

Mathematica

(* For any individual n *) k = 17; While[ !PrimeQ[k] || PowerMod[10, 10^100, k] - n != 0, k += 2]; k

PARI

a(n) = forprime(p=17, oo, if(Mod(10, p)^lift(Mod(10, p-1)^100) == n, return(p))); \\ Jinyuan Wang, Apr 17 2020

Extensions

Name edited by Peter Munn, Feb 20 2025