A078813 Smallest prime factor of googol - n that exceeds 13, or 1 if googol - n is 13-smooth.

1, 41, 220217, 596275259857, 17, 31, 7583, 167988019, 1898431, 19, 37, 8747, 433, 23, 4647535350279428239, 1637, 29, 1997, 569, 383, 71, 17, 179, 683592593118601, 601, 1259, 109, 47, 19, 83, 367, 43, 151, 8633431, 103, 20859069935591, 23

Offset: 0

Author

Robert G. Wilson v, Dec 06 2002

Keywords

• nonn

Examples

			From _Zhuorui He_, Jul 15 2025: (Start)
Googol = 10^100 = 2^100 * 5^100 is 13-smooth so a(0)=1.
10^100 - 1 = 3^2 * 11 * 41 * 101 * 251 * 271 * ... so a(1)=41. (End)
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 0..1000
• Dario Alejandro Alpern, Factors of 1000 numbers starting from googolplex
• Robert Harley, Factors of Googolplex+1
• Eric Weisstein's World of Mathematics, Googol

Crossrefs

Cf. A108251 (n such that googol - n is prime), A080197 (relates to positions of 1's).

Equivalent sequences: A076848 (googol + n), A078814 (googolplex - n).

See the formula section for the relationships with A007947, A020639, A034386.

Programs

PARI

/* using M. F. Hasler's definition for A020639 */
A078813(n)={n=10^100-n; my(p=[2,3,5,7,11,13]); for(i=1, 6, n=n/(p[i]^valuation(n,p[i]))); A020639(n)} /* Zhuorui He , Jul 17 2025 */

Formula

For n >= 1, a(n) = A020639(A007947(10^100 - n)/gcd(10^100 - n, A034386(13))), where A020639(m) = lpf(m), smallest prime factor of m. - Peter Munn, Feb 20 2025

a(-n) = A076848(n). - Zhuorui He, Jul 15 2025

Extensions

Name edited by Peter Munn, Feb 20 2025

a(0) prepended by Zhuorui He, Jul 15 2025