A231901 -id:A231901 - cp's OEIS frontend

A231549 Least k>0 such that k!*n!+1 is a prime, or 0 if no such k exists.

1, 1, 1, 4, 2, 8, 3, 3, 3, 4, 1, 2, 3, 5, 8, 4, 10, 2, 11, 9, 5, 5, 7, 3, 14, 18, 1, 40, 24, 5, 5, 18, 8, 20, 2, 49, 1, 3, 5, 28, 1, 17, 38, 27, 11, 16, 10, 3, 24, 270, 2, 45, 2, 15, 175, 64, 17, 6, 4, 3, 8, 18, 13, 17, 65, 32, 12, 7, 72, 13, 21, 33, 1, 24, 36, 76, 1

Offset: 1

Alex Ratushnyak, Nov 15 2013

nonn

Indices of 1's: A002981.

Cf. A002981, A035093, A057217, A075757, A075758, A231901.

Table[k = 1; While[! PrimeQ[k!*n! + 1], k++]; k, {n, 100}] (* T. D. Noe, Nov 18 2013 *)

A238505 a(n) is the minimum number such that a(n)!/n! - 1 is prime (or 0 if no such number exists).

Original entry on oeis.org

3, 3, 3, 4, 6, 6, 9, 8, 10, 11, 12, 12, 14, 14, 16, 17, 19, 18, 20, 20, 22, 24, 25, 24, 41, 27, 30, 29, 34, 30, 32, 32, 42, 36, 36, 44, 39, 38, 40, 42, 42, 42, 46, 44, 46, 47, 49, 48, 52, 51, 58, 58, 54, 54, 56, 57, 59, 60, 60, 60, 71, 62, 65, 65, 66, 67, 71

Offset: 0

Lei Zhou, Feb 27 2014

nonn

If a(n) = 0, all numbers m!/n! - 1 for integer m > n are composite.

Up to n = 2500, a(n) > 0.

			n = 1: 2!/1! - 1 = 1 is not prime, 3!/1! - 1 = 5 is prime.  So a(1) = 3;
n = 6: 7!/6! - 1 = 6, 8!/6! - 1 = 55, 9!/6! - 1 = 503.  6 and 55 are not prime.  503 is prime.  So a(6) = 9.

Lei Zhou, Table of n, a(n) for n = 0..2500

Cf. A000142, A231901

Table[i = n; a = n;  While[! PrimeQ[a - 1], i++; a = a*i]; i, {n, 1, 67}]

a(n) = {m = n; while(! isprime(m!/n! -1), m++); m;} \\ Michel Marcus, Mar 06 2014

cp's OEIS Frontend

A231549 Least k>0 such that k!*n!+1 is a prime, or 0 if no such k exists.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica