A059803 Numbers k such that 9^k - 8^k is prime.

2, 7, 29, 31, 67, 149, 401, 2531, 19913, 30773, 53857, 170099

Offset

1,1

Comments

Some of the larger entries may only correspond to probable primes.

In general, for any positive integers m, a and b, a > b, a necessary condition for a^m - b^m to be prime is that either a-b = 1 and m is prime or m = 1 and a-b is prime (from Arturo Magidin and Hagman in Sci.Math, Sep 11, 2010). - Vincenzo Librandi, Sep 12 2010

Links

Table of n, a(n) for n=1..12.

Prog

(PARI) is(n)=ispseudoprime(9^n-8^n) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

Cf. A000043, A057468, A059801, A059802, A062572-A062574, A062576-A062666.

Sequence in context: A122118 A337429 A388658 * A076043 A180448 A396453

Adjacent sequences: A059800 A059801 A059802 * A059804 A059805 A059806

Keyword

nonn,hard

Author

Mike Oakes, Feb 23 2001

Extensions

Three more terms found by Jean-Louis Charton in 2004-2005: a(9) = 30773, a(10) = 53857, a(11) = 170099. - Alexander Adamchuk, Dec 08 2006

Status

approved