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A242928
Least number k such that (k^k+n^n)/(k+n) is prime or 0 if no such k exists.
0
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, 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, 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
OFFSET
1,1
COMMENTS
If a(i) = j, then a(j) <= i for all i and j.
a(n) = 0 is confirmed for k <= 2500. These are just conjectural.
EXAMPLE
(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.
PROG
(PARI) a(n)=for(k=1, 2500, s=(k^k+n^n)/(k+n); if(floor(s)==s, if(ispseudoprime(s), return(k))))
n=1; while(n<100, print(a(n)); n+=1)
CROSSREFS
Sequence in context: A171839 A257778 A325111 * A214845 A366766 A071960
KEYWORD
nonn,hard,more
AUTHOR
Derek Orr, May 26 2014
EXTENSIONS
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
STATUS
approved