login
Smallest prime of the form n^k - k^n for some k, or 0 if no such prime exists.
1

%I #24 Aug 11 2014 23:38:27

%S 7,2,3,6102977801,5,79792265017612001,7,2486784401

%N Smallest prime of the form n^k - k^n for some k, or 0 if no such prime exists.

%C Conjecture: a(n) > 0 for all n not in A097764.

%C More terms in b-file. If n > 4 and in A097764, n^k - k^n is factorable and won't be prime.

%C a(17) > 17^7500 - 7500^17. See A239279.

%H Derek Orr, <a href="/A241427/b241427.txt">Table of n, a(n) for n = 2..16</a>

%o (PARI)

%o a(n)=k=1;if(n>4,forprime(p=1,100,if(ispower(n)&&ispower(n)%p==0&&n%p==0,return(0));if(n%p==n,break)));k=1;while(!ispseudoprime(n^k-k^n),k++);return(n^k-k^n)

%o vector(15, n, a(n+1))

%Y Cf. A078201.

%K nonn

%O 2,1

%A _Derek Orr_, Aug 08 2014