%I #32 Jan 13 2019 06:00:08
%S 3,17,23,29,47,61,1619,18251,106187,201653,1178033
%N Numbers n such that (7^n + 1)/8 is a prime.
%C (7^1619+1)/8, a 1368-digit number, has been certified prime with Primo. - _Rick L. Shepherd_, May 19 2002
%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 and T. Granlund, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL3/DUBNER/dubner.html">Primes of the Form (b^n+1)/(b+1)</a>, J. Integer Sequences, 3 (2000), #P00.2.7.
%H H. Lifchitz, <a href="http://www.primenumbers.net/Henri/us/MersFermus.htm">Mersenne and Fermat primes field</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Repunit.html">Repunit</a>
%t lst={};Do[p=(7^n+1)/8;If[PrimeQ[p], AppendTo[lst, n]], {n, 7!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Sep 29 2008 *)
%o (PARI) isok(n) = (denominator(p=(7^n+1)/8)==1) && isprime(p); \\ _Michel Marcus_, Oct 30 2017
%K nonn,more
%O 1,1
%A _N. J. A. Sloane_, Sep 15 2000
%E a(9)=106187 is a probable prime based on Fermat primality testing and trial factoring to 2E13. - _Paul Bourdelais_, Apr 07 2008
%E a(10)=201653 is a probable prime discovered by _Paul Bourdelais_, Feb 17 2010
%E a(11)=1178033 corresponds to a probable prime discovered by _Paul Bourdelais_, Jan 11 2019