A245695 - OEIS

%I #12 Jul 30 2014 08:16:32

%S 1,2,0,4,25,42,49,88,207,170,121,12,377,938,285,688,391,558,703,1780,

%T 609,682,713,2328,3275,1066,1593,28,1943,6690,3317,4064,2607,1258,

%U 3395,2196,4847,38,1677,3880,2173,42,4171,3124,2115,10994,4747,11184,2597,4150,3111,14092,2809,3834,12265,3976,8493,6206,16697,17580,16531,47678,8253,17344,4355,12738,18961,4964,5727,9170,9869,61704,7373

%N Least number k >= 0 such that (n!+k)/n is prime.

%C a(n) = M*n for some integer M >= 0.

%C a(n) = n times least m >= 0 such that (n-1)!+m is prime. - _Jens Kruse Andersen_, Jul 30 2014

%H Jens Kruse Andersen, <a href="/A245695/b245695.txt">Table of n, a(n) for n = 1..2001</a>

%F a(n) = n*A033932(n-1), except a(3) = 0 where A033932 demands positive values. - _Jens Kruse Andersen_, Jul 30 2014

%e (4!+0)/4 = 6 is not prime.

%e (4!+1)/4 = 25/4 is not prime.

%e (4!+2)/4 = 26/4 is not prime.

%e (4!+3)/4 = 27/4 is not prime.

%e (4!+4)/4 = 7 is prime. Thus a(4) = 4.

%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=1;while(n<100,print1(a(n),", ");n++)

%Y Cf. A033932, A245696, A245697.

%K nonn

%O 1,2

%A _Derek Orr_, Jul 29 2014