A059803 Numbers n such that 9^n - 8^n is prime or a strong pseudoprime.

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

Offset: 1

Author

Mike Oakes, Feb 23 2001

Keywords

• nonn
• hard

Comments

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

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

Crossrefs

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

Programs

PARI

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

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