A242796 Least number k such that (k^k-n)/(k-n) is prime, or 0 if no such k exists.

2, 4, 6, 5, 0, 13, 9, 11, 0, 12, 22, 13, 37, 28, 36, 0, 0, 171, 73, 85, 0, 0, 0, 29, 0, 0, 0, 0, 517, 35, 40, 49, 44, 49, 0, 41, 46, 40, 0, 0, 51, 0, 52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2841, 0, 0, 0, 0, 0, 0, 67, 0, 64, 0, 199, 125, 221, 0, 0, 153, 113, 239, 0, 97, 0, 0, 0

Offset

1,1

Comments

a(n)=0 is confirmed for k <= 5000.

Links

Table of n, a(n) for n=1..76.

Example

(1^1-2)/(1-2) = 1 is not prime. (3^3-2)/(3-2) = 25 is not prime. (4^4-2)/(4-2) = 254/2 = 127 is prime. Thus a(2) = 4.

Prog

(PARI) a(n)=for(k=1, 5000, if(k!=n, s=(k^k-n)/(k-n); if(floor(s)==s, if(ispseudoprime(s), return(k)))));
n=1; while(n<100, print(a(n)); n+=1)

Crossrefs

Cf. A242787, A242788.

Sequence in context: A365160 A082747 A127275 * A298527 A071288 A063892

Adjacent sequences: A242793 A242794 A242795 * A242797 A242798 A242799

Keyword

nonn,more,hard

Author

Derek Orr, May 22 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