A076848 Smallest prime factor of googol + n that exceeds 13, or 1 if googol + n is 13-smooth.

73, 4832936419, 157, 20794121, 127, 859493, 557, 113, 3221, 19, 7549, 43, 17, 61, 211, 241, 18617, 907, 419, 47, 443, 911, 47955653711170550856726386495271851, 1109, 53, 31, 37, 2543, 19, 17, 617, 33521, 23, 7906914473, 38851, 421, 39640576062095087

Offset: 1

Author

Jason Earls, Nov 23 2002

Keywords

• nonn

Comments

A googol is 10^100. Factors found using PARI and Dario Alpern's ECM factorization applet.

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..1000 (terms 1..400 from Charles R Greathouse IV, n=260 corrected by Sean A. Irvine)
• Dario Alpern, Factorization using the Elliptic Curve Method

Crossrefs

Cf. A049014 (n such that googol + n is prime), A066298, A080197 (relates to positions of 1's).

Equivalent sequences: A072288 (googolplex + n), A078813 (googol - n).

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

Formula

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

Extensions

a(23) found by Sean A. Irvine on Dec 08 2002 by employing SNFS, using the polynomials x^5+23 and x-10^20.

Edited by Robert G. Wilson v, Dec 09 2002

Edited by Peter Munn, Feb 20 2025