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%I #35 Jul 09 2023 16:27:27
%S 3,43,113,157,269,709,1109,2027,8297,86837,310721
%N Numbers k such that 81^k - 80^k is prime.
%C Terms greater than 1000 are often only strong pseudoprimes.
%C a(11) > 10^5. - _Robert Price_, Jan 13 2015
%C Factors of these numbers are of the form p = 2*n*k + 1, just like the repunit numbers, but the PRP tests are significantly slower since there is not a fast mod() property like the repunits, where (number mod Rn) can be calculated with a folding of the digits at length n in base b. However, numbers of this form b^p - (b-1)^p seem to be prime with greater relative frequency than the repunits. While the repunits have a linear fit coefficient that approaches 0.56145948 (see link below for a Generalized Repunit Conjecture), this sequence currently has a linear fit coefficient of 0.22559. - _Paul Bourdelais_, Jul 06 2023
%H Paul Bourdelais, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;417ab0d6.0906">A Generalized Repunit Conjecture</a>
%o (PARI) is(n)=ispseudoprime(81^n-80^n) \\ _Charles R Greathouse IV_, Jun 12 2017
%Y Cf. A000043, A057468, A059801, A059802, A062572-A062666.
%K nonn,hard,more
%O 1,1
%A _Mike Oakes_, May 18 2001, May 19 2001
%E a(10) from _Robert Price_, Jan 13 2015 (Computer run by Adam Marciniec)
%E a(11) from _Paul Bourdelais_, Jul 06 2023
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