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Numbers n such that (15^n - 1)/14 is prime.
(Formerly M3150)
13

%I M3150 #52 Apr 22 2019 13:51:00

%S 3,43,73,487,2579,8741,37441,89009,505117,639833

%N Numbers n such that (15^n - 1)/14 is prime.

%C 8741 and 37441 are only probable primes. - Julien Peter Benney (jpbenney(AT)ftml.net), Apr 27 2007

%D Paulo Ribenboim, "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 P. Bourdelais, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;417ab0d6.0906">A Generalized Repunit Conjecture</a>

%H Harvey 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 Henri Lifchitz, <a href="http://www.primenumbers.net/Henri/us/MersFermus.htm">Mersenne and Fermat primes field</a>

%H <a href="/index/Pri#primepop">Index to primes in various ranges</a>, form ((k+1)^n-1)/k

%e (15^3 - 1)/14 = 241, which is prime.

%t lst={};Do[If[PrimeQ[(15^n-1)/14], Print[n];AppendTo[lst, n]], {n, 10^5}];lst (* _Vladimir Joseph Stephan Orlovsky_, Aug 21 2008 *)

%o (PARI) is(n)=ispseudoprime((15^n-1)/14) \\ _Charles R Greathouse IV_, Apr 29 2015

%Y Cf. A059802, A062647, A003525.

%K nonn,hard,more

%O 1,1

%A _N. J. A. Sloane_

%E a(7) from Julien Peter Benney (jpbenney(AT)ftml.net), Apr 27 2007

%E a(8) corresponds to a probable prime discovered by _Paul Bourdelais_, Mar 15 2010

%E a(9) corresponds to a probable prime discovered by _Paul Bourdelais_, Jan 14 2015

%E a(10) corresponds to a probable prime discovered by _Paul Bourdelais_, Apr 22 2019