A078814 -id:A078814 - cp's OEIS frontend

A072288 Smallest prime factor of googolplex + n that exceeds 13, or 1 if googolplex + n is 13-smooth.

316912650057057350374175801344000001

Offset: 1

Ed Pegg Jr and Robert G. Wilson v, Nov 21 2002

a(2) is not known. After a(1) the sequence continues ?, 1429, 1129, 29, ?, 53, 427169, 5501, 19, 59, 1327, 1645318771, 61, 211, 17, 1831, ?, 43, 389, 173, 233886337, 139, 1451, 18797, 31, 37, 8297, 19, 13879, ?, 9241, 17, 29, ...

The question marks indicate terms > 10^14. - Dario Alpern, May 17 2003

Tanya Khovanova, Non Recursions
Dario Alejandro Alpern, Factors of 1000 numbers starting from googolplex
Robert Harley, Factors of Googolplex+1 (Found some terms)
Eric Weisstein's World of Mathematics, Googolplex
Index entries for one-term sequences

Cf. A067007, A078814, A341116.

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

Name edited by Peter Munn, Feb 20 2025

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

Original entry on oeis.org

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

Robert G. Wilson v, Dec 06 2002

nonn

			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)

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

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.

/* 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 */

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

Name edited by Peter Munn, Feb 20 2025

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

cp's OEIS Frontend

A072288 Smallest prime factor of googolplex + n that exceeds 13, or 1 if googolplex + n is 13-smooth.

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