A242915 - OEIS

%I #11 Oct 08 2015 01:21:54

%S 2,4,5,125

%N Numbers n such that (n!-k!)/(n-k) is prime for some k.

%C a(5) > 1000.

%C The n-values not listed have been checked for k <= 5000.

%C The number k that corresponds to {2, 4, 5, 125} is {4, 2, 125, 5} respectively.

%C Let S = (k!-n!)/(k-n). If n is in the sequence and k is the least number that makes S prime (using n), then n` = k is also in the sequence and k` = n is the least number that makes S prime (using n`).

%e (4!-k!)/(4-k) is prime for some k (namely, k = 2). Thus 4 is a member of this sequence.

%o (PARI) a(n)=for(k=1,5000,if(k!=n,s=(n!-k!)/(n-k); if(floor(s)==s&&ispseudoprime(s),return(k))))

%o n=1;while(n<1000,if(a(n),print1(n,", "));n+=1)

%K nonn,hard,more

%O 1,1

%A _Derek Orr_, May 26 2014