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Numbers n such that (17^n-1)/16 is prime.
(Formerly M2415)
12

%I M2415 #27 Aug 03 2020 08:50:57

%S 3,5,7,11,47,71,419,4799,35149,54919,74509,1990523

%N Numbers n such that (17^n-1)/16 is prime.

%C No others for any n less than 8447. - Julien Peter Benney (jpbenney(AT)ftml.net), Aug 15 2004

%D Ribenboim, Paulo; "The Book Of Prime Number Records"; published 1989 by Springer-Verlag; pages 350-354.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%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>

%t lst={};Do[If[PrimeQ[(17^n-1)/16], Print[n];AppendTo[lst, n]], {n, 10^5}];lst (* _Vladimir Joseph Stephan Orlovsky_, Aug 21 2008 *)

%o (PARI) is(n)=isprime((17^n-1)/16) \\ _Charles R Greathouse IV_, Apr 28 2015

%K hard,nonn,more

%O 1,1

%A _N. J. A. Sloane_

%E a(9)=35149 & a(10)=54919 are probable primes discovered by _Paul Bourdelais_, Mar 08 2010

%E a(11)=74509 is a probable prime discovered by _Paul Bourdelais_, Mar 10 2010

%E a(12)=1990523 corresponds to a probable prime discovered by _Paul Bourdelais_, Aug 03 2020