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%I #14 Jan 30 2023 12:30:29
%S 0,4,5,42,7,8,279,130,121,156,13,322,15,752,901,1062,779,2020,651,682,
%T 1679,2136,1825,3874,999,1204,2929,930,31,1952,33,34,6755,4068,4699,
%U 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
%N Least number k >= 0 such that (n!-k)/n is prime.
%C a(n) < n! for all n > 2.
%C 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.)
%H Jens Kruse Andersen, <a href="/A245696/b245696.txt">Table of n, a(n) for n = 3..2001</a>
%e (6!-42)/6 = 113 is prime. Since 42 is the smallest number to produce a prime, a(6) = 42.
%t lnk[n_]:=Module[{k=0},While[!PrimeQ[(n!-k)/n],k++];k]; Array[lnk,80,3] (* _Harvey P. Dale_, Jan 30 2023 *)
%o (PARI)
%o a(n)=for(k=0,10^6,s=(n!-k)/n;if(floor(s)==s,if(ispseudoprime(s),return(k))))
%o n=3;while(n<100,print1(a(n),", ");n++)
%Y Cf. A033933, A245695, A245697.
%K nonn
%O 3,2
%A _Derek Orr_, Jul 29 2014
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