A242922 Least number k such that (k^n+n^k)/(k+n) is prime or 0 if no such k exists.

0, 2, 8, 0, 0, 0, 43, 3, 0, 0, 0, 0, 21, 0, 0, 0, 0, 0, 0, 0, 13, 0, 47, 0, 287, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 23, 0, 0, 0, 0, 0, 77, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1795, 0, 0, 0, 0, 0, 0, 0, 0, 0, 53, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,2

Comments

If a(i) = j, then a(j) = i for any i and j.

a(n) = 0 is definite for n=1. For other n-values where a(n) = 0, it is confirmed for k <= 5000. These are only conjectural.

Links

Table of n, a(n) for n=1..88.

Example

(8^3+3^8)/(8+3) = 7073/11 = 643 is prime. Thus, a(3) = 8 and a(8) = 3.

Prog

(PARI) a(n)=for(k=1, 5000, s=(k^n+n^k)/(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: A246516 A095217 A230915 * A242530 A073410 A021361

Adjacent sequences: A242919 A242920 A242921 * A242923 A242924 A242925

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