cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A049014 n plus a googol is prime.

Original entry on oeis.org

267, 949, 1243, 1293, 1983, 2773, 2809, 2911, 2967, 3469, 3501, 3799, 4317, 4447, 4491, 5383, 5641, 5949, 6403, 6637, 6903, 7443, 8583, 8653, 9013, 9223, 9259, 9631, 10071, 10557, 10833, 10903, 11143, 11173, 11529, 11667, 11839, 12207, 12817
Offset: 1

Views

Author

G. L. Honaker, Jr.

Keywords

Comments

10^100 + a(135) and 10^100 + a(136) are the first twin primes greater than 10^100. - T. D. Noe, Nov 03 2008
For each of the 1000 terms in the table, 10^100 + a(n) was verified by the Magma calculator (http://magma.maths.usyd.edu.au/calc/) as prime. - Jon E. Schoenfield, Aug 24 2009

Links

Crossrefs

Cf. A108251, A133281.

Extensions

Terms greater than 267 found by Carlos Rivera

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

Views

Author

Robert G. Wilson v, Dec 06 2002

Keywords

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

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
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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