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 1-1 of 1 results.

A193447 a(n) = ((p - 2)! + p - 1)/(p*(p - 1)) where p is the n-th prime.

Original entry on oeis.org

3, 3299, 255877, 4807626353, 1040021719579, 100970241446066087, 13409937746820630739862069, 9507270961010432209186683871, 7757618593382991688938927430572972973, 12437732976339904486975781548721278876097561, 18522993694996570934756402022946152638511627907
Offset: 4

Views

Author

Alzhekeyev Ascar M, Jul 26 2011

Keywords

Comments

Conjecture: for k >= 7, ((k - 2)! + k - 1)/(k*(k - 1)) is an integer iff k is prime.
Proof follows from Wilson's theorem. - Alois P. Heinz, Aug 07 2011
Note that a(1) = 1 is also an integer. - Jianing Song, Sep 17 2018

Examples

			a(4) = (5! + 6)/(7*6) = 126/42 = 3.
a(5) = (9! + 10)/(11*10) = 362890/110 = 3299.

Links

Crossrefs

Cf. A000040, A007619, A066161.

Programs

  • PARI
    a(n) = my(p=prime(n)); ((p-2)!+p-1)/(p*(p-1)) \\ Jianing Song, Sep 17 2018

Extensions

Name clarified by Jianing Song, Sep 17 2018
Showing 1-1 of 1 results.

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

Content is available under The OEIS End-User License Agreement.