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%I M0744 #51 Oct 16 2023 22:23:35
%S 2,3,5,19,97,109,317,353,701,9739,14951,37573,46889,769543
%N Numbers k such that (12^k - 1)/11 is prime.
%C Also, numbers k such that 12^k-1 is a semiprime. - _Sean A. Irvine_, Oct 16 2023
%D J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and later supplements.
%D J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 109, p. 38, Ellipses, Paris 2008.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H P. Bourdelais, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;417ab0d6.0906">A Generalized Repunit Conjecture</a>
%H J. Brillhart et al., <a href="http://dx.doi.org/10.1090/conm/022">Factorizations of b^n +- 1</a>, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
%H H. Dubner, <a href="http://dx.doi.org/10.1090/S0025-5718-1993-1185243-9">Generalized repunit primes</a>, Math. Comp., 61 (1993), 927-930.
%H H. Dubner, <a href="/A028491/a028491.pdf">Generalized repunit primes</a>, Math. Comp., 61 (1993), 927-930. [Annotated scanned copy]
%H H. Lifchitz, <a href="http://www.primenumbers.net/Henri/us/MersFermus.htm">Mersenne and Fermat primes field</a>
%H S. S. Wagstaff, Jr., <a href="http://www.cerias.purdue.edu/homes/ssw/cun/index.html">The Cunningham Project</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Repunit.html">Repunit</a>
%t lst={}; Do[If[PrimeQ[(12^n-1)/11], Print[n]; AppendTo[lst, n]], {n, 10^5}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Aug 21 2008 *)
%o (PARI) is(n)=ispseudoprime((12^n-1)/11) \\ _Charles R Greathouse IV_, Apr 29 2015
%K nonn,hard
%O 1,1
%A _N. J. A. Sloane_
%E a(11) from _Paul Bourdelais_, Aug 03 2007
%E One more term from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008
%E a(13)=46889, discovered Sep 10 2008 by Paul Bourdelais, corresponds to a probable prime based on trial factoring to 10^13 and Fermat base 2 primality test. - _Paul Bourdelais_, Sep 11 2008
%E a(14)=769543 corresponds to a probable prime discovered by _Paul Bourdelais_, Dec 05 2014
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