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

0,2

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

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

Example

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)

Prog

(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 */

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.

Sequence in context: A214163 A185539 A214184 * A214235 A112550 A114927

Adjacent sequences: A078810 A078811 A078812 * A078814 A078815 A078816

Keyword

nonn

Author

Robert G. Wilson v, Dec 06 2002

Extensions

Name edited by Peter Munn, Feb 20 2025

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

Status

approved