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

1,1

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

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: A321181 A122118 A337429 * A076043 A180448 A116968

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