A057172 - OEIS

%I #31 Aug 20 2021 10:02:17

%S 3,11,31,43,47,59,107,811,2819,4817,9601,33581,38447,41341,131891,

%T 196337,1313371

%N Numbers n such that (6^n + 1)/7 is a prime.

%C a(15), a(16) and a(17) correspond to probable primes.

%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 Select[Range[5000], PrimeQ[(6^# + 1) / 7] &] (* _Vincenzo Librandi_, Oct 29 2017 *)

%o (PARI) isok(n) = (denominator(p=(6^n+1)/7)==1) && isprime(p); \\ _Michel Marcus_, Oct 29 2017

%K nonn,more

%O 1,1

%A _N. J. A. Sloane_, Sep 15 2000

%E a(12) was discovered by Kamil Duszenko, Jul 15 2003

%E a(13) was discovered by _Henri Lifchitz_, Sep 15 2007

%E a(14) was discovered by _Paul Bourdelais_, Oct 01 2007

%E a(15) was discovered by _Paul Bourdelais_, Feb 01 2010

%E a(16) was discovered by _Paul Bourdelais_, Feb 19 2010

%E a(17) was discovered by _Paul Bourdelais_, Jan 28 2019