

A057172


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


14



3, 11, 31, 43, 47, 59, 107, 811, 2819, 4817, 9601, 33581, 38447, 41341, 131891, 196337, 1313371
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OFFSET

1,1


COMMENTS

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


LINKS

Table of n, a(n) for n=1..17.
P. Bourdelais,A Generalized Repunit Conjecture
J. Brillhart et al., Factorizations of b^n + 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
H. Lifchitz, Mersenne and Fermat primes field
Eric Weisstein's World of Mathematics, Repunit


MATHEMATICA

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


PROG

(PARI) isok(n) = (denominator(p=(6^n+1)/7)==1) && isprime(p); \\ Michel Marcus, Oct 29 2017


CROSSREFS

Sequence in context: A018781 A119215 A266970 * A277167 A277049 A261148
Adjacent sequences: A057169 A057170 A057171 * A057173 A057174 A057175


KEYWORD

nonn,more


AUTHOR

N. J. A. Sloane, Sep 15 2000


EXTENSIONS

a(12) was discovered by Kamil Duszenko, Jul 15 2003
a(13) was discovered by Henri Lifchitz, Sep 15 2007
a(14) was discovered by Paul Bourdelais, Oct 01 2007
a(15) was discovered by Paul Bourdelais, Feb 01 2010
a(16) was discovered by Paul Bourdelais, Feb 19 2010
a(17) was discovered by Paul Bourdelais, Jan 28 2019


STATUS

approved



