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

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

0,1

Comments

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

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

Links

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A000142, A231901

Sequence in context: A334940 A011978 A167025 * A259897 A091849 A035567

Adjacent sequences: A238502 A238503 A238504 * A238506 A238507 A238508

Keyword

nonn

Author

Lei Zhou, Feb 27 2014

Status

approved