A242928 Least number k such that (k^k+n^n)/(k+n) is prime or 0 if no such k exists.

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.

Links

Table of n, a(n) for n=1..99.

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

Adjacent sequences: A242925 A242926 A242927 * A242929 A242930 A242931

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