A245696 Least number k >= 0 such that (n!-k)/n is prime.

0, 4, 5, 42, 7, 8, 279, 130, 121, 156, 13, 322, 15, 752, 901, 1062, 779, 2020, 651, 682, 1679, 2136, 1825, 3874, 999, 1204, 2929, 930, 31, 1952, 33, 34, 6755, 4068, 4699, 3686, 39, 2920, 3403, 5502, 3397, 4796, 4905, 2438, 4183, 3792, 5047, 2950, 4947, 9308, 3551, 3186, 6985, 3416, 26277, 16066, 6431, 8220, 8479, 4402, 4473, 6464, 23335, 8382, 21239, 12988, 17319, 7210, 6887, 54072, 11899, 27602

Offset: 3

Author

Derek Orr, Jul 29 2014

Keywords

• nonn

Comments

a(n) < n! for all n > 2.

a(n) = n times (least m >= 0 such that (n-1)!-m is prime) = n*A033933(n-1). - Jens Kruse Andersen, Jul 30 2014 (This shows that a(n) always exists.)

Examples

			(6!-42)/6 = 113 is prime. Since 42 is the smallest number to produce a prime, a(6) = 42.
		

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 3..2001

Crossrefs

Cf. A033933, A245695, A245697.

Programs

Mathematica

lnk[n_]:=Module[{k=0},While[!PrimeQ[(n!-k)/n],k++];k]; Array[lnk,80,3] (* Harvey P. Dale, Jan 30 2023 *)

PARI

a(n)=for(k=0,10^6,s=(n!-k)/n;if(floor(s)==s,if(ispseudoprime(s),return(k))))
n=3;while(n<100,print1(a(n),", ");n++)