A245634 Least number k such that (n^k-k^n)/(k-n) is prime, or 0 if no such number exists.

0, 6, 4, 3, 3, 2, 3, 0, 5, 7, 3, 13, 11, 0, 17, 0, 15, 0, 7, 0, 0, 15, 5, 0, 79, 0, 0, 0, 15, 0, 0, 0, 65, 0, 47, 0, 39, 0, 37, 0, 9, 0, 0, 45, 44, 0, 11, 0, 103, 0, 71, 0, 11, 0, 119, 0, 5, 0, 0, 0, 0, 0, 0, 0, 33, 0, 75, 0, 77, 0, 51, 143, 0, 0, 67, 0, 69, 0, 25, 0, 131, 0, 0, 0, 57, 0, 8887, 0, 221, 0, 291, 0, 0, 0, 0, 0, 101, 0, 0

Offset

1,2

Comments

a(1) = 0 is the only confirmed 0 in this sequence.

a(n) = 0 for n > 1 is confirmed for k < 10000.

If a(n) = m, then a(m) <= n for m > 0 and n > 0.

Links

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

Example

(2^1-1^2)/(1-2) = -1 is not prime.
(2^3-3^2)/(3-2) = -1 is not prime.
(2^4-4^2)/(4-2) = 0 is not prime.
(2^5-5^2)/(5-2) = 7/3 is not prime.
(2^6-6^2)/(6-2) = 7 is prime. Thus a(2) = 6.

Prog

(PARI)
a(n)=for(k=1, 10^4, if(k!=n, s=(n^k-k^n)/(k-n); if(floor(s)==s, if(ispseudoprime(s), return(k)))))
n=1; while(n<100, print1(a(n), ", "); n++)

Crossrefs

Cf. A242922.

Sequence in context: A329081 A343461 A155044 * A182618 A118227 A199429

Adjacent sequences: A245631 A245632 A245633 * A245635 A245636 A245637

Keyword

nonn

Author

Derek Orr, Jul 28 2014

Status

approved