cp's OEIS Frontend

A004063 Numbers k such that (7^k - 1)/6 is prime.

%I A004063 M3836 #58 Apr 25 2025 05:26:38
%S A004063 5,13,131,149,1699,14221,35201,126037,371669,1264699
%N A004063 Numbers k such that (7^k - 1)/6 is prime.
%C A004063 Base-7 repunit primes. - _Paul Bourdelais_, Aug 31 2007
%C A004063 Among repunits with bases from -11 to 11, base-7 repunits have the lowest relative rate of occurrence of primes so far. - _Paul Bourdelais_, Feb 23 2010
%D A004063 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 A004063 Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 236.
%D A004063 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A004063 Paul Bourdelais, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;417ab0d6.0906">A Generalized Repunit Conjecture</a>
%H A004063 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 A004063 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 A004063 H. Dubner, <a href="/A028491/a028491.pdf">Generalized repunit primes</a>, Math. Comp., 61 (1993), 927-930. [Annotated scanned copy]
%H A004063 H. Lifchitz, <a href="http://www.primenumbers.net/Henri/us/MersFermus.htm">Mersenne and Fermat primes field</a>
%H A004063 S. S. Wagstaff, Jr., <a href="http://www.cerias.purdue.edu/homes/ssw/cun/index.html">The Cunningham Project</a>
%H A004063 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Repunit.html">Repunit</a>
%t A004063 For[n = 1, n <= 20000, n++, If[PrimeQ[(7^n - 1)/6 ], Print[n]]] (* Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 09 2006 *)
%o A004063 (Prime95) PRP=1,7,1264699,-1,0,0,"6"
%o A004063 (PARI) is(n)=isprime((7^n - 1)/6) \\ _Charles R Greathouse IV_, Apr 28 2015
%K A004063 nonn,hard,more
%O A004063 1,1
%A A004063 _N. J. A. Sloane_
%E A004063 a(6) from _Robert G. Wilson v_, Apr 09 2005
%E A004063 a(7) is a probable prime from _Paul Bourdelais_, Aug 31 2007
%E A004063 a(8) discovered Sep 17 2008 by Paul Bourdelais & Eric Purohit - it is a probable prime based on trial factoring to 2.5*10^13 and Fermat base 2 primality test. - _Paul Bourdelais_, Sep 18 2008
%E A004063 a(9) is a probable prime discovered by _Paul Bourdelais_, Feb 23 2010
%E A004063 a(10) is a probable prime discovered by _Paul Bourdelais_, Jan 06 2014