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A059803 Numbers n such that 9^n - 8^n is prime or a strong pseudoprime. 13

%I #21 Jun 13 2017 16:39:39

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

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

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

%C 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

%o (PARI) is(n)=ispseudoprime(9^n-8^n) \\ _Charles R Greathouse IV_, Jun 13 2017

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

%K nonn,hard

%O 1,1

%A _Mike Oakes_, Feb 23 2001

%E 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

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Last modified April 25 01:35 EDT 2024. Contains 371964 sequences. (Running on oeis4.)