A242928 - OEIS

%I #12 Oct 21 2014 12:39:23

%S 3,2,1,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,151,0,0,

%T 0,17,0,53,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,37,0,103,0,0,0,0,0,0,0,0,0,0,

%U 0,0,0,0,0,97,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,137,0,0,0,71,0,0

%N Least number k such that (k^k+n^n)/(k+n) is prime or 0 if no such k exists.

%C If a(i) = j, then a(j) <= i for all i and j.

%C a(n) = 0 is confirmed for k <= 2500. These are just conjectural.

%e (1^1+1^1)/(1+1) = 1 is not prime. (2^2+1^1)/(2+1) = 5/3 is not prime. (3^3+1^1)/(3+1) = 7 is prime. Thus, a(3) = 1 and a(1) = 3.

%o (PARI) a(n)=for(k=1,2500,s=(k^k+n^n)/(k+n);if(floor(s)==s,if(ispseudoprime(s),return(k))))

%o n=1;while(n<100,print(a(n));n+=1)

%K nonn,hard,more

%O 1,1

%A _Derek Orr_, May 26 2014

%E We don't normally allow conjectural terms, except in special circumstances. This is one of those exceptions, for if we included only terms that are known for certain, not much of this sequence would remain. - _N. J. A. Sloane_, May 31 2014