

A057171


Numbers n such that (5^n+1)/6 is a prime.


34



5, 67, 101, 103, 229, 347, 4013, 23297, 30133, 177337, 193939, 266863, 277183, 335429
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OFFSET

1,1


COMMENTS

With the discovery of a(13), the best fit line slope G=0.59823 (see link to Generalized Repunit Conjecture). This sequence is converging nicely to the conjectured slope G=0.56145948.  Paul Bourdelais, Jul 16 2010
With the discovery of a(14), the best fit line slope G=0.56243 (see link to Generalized Repunit Conjecture). This sequence is converging nicely to the conjectured slope G=0.56145948.  Paul Bourdelais, Aug 23 2010


LINKS

Table of n, a(n) for n=1..14.
Paul 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
R. G. Wilson, v, Letter to N. J. A. Sloane, circa 1991.


MATHEMATICA

a={}; Do[x=(5^n+1)/6; If[PrimeQ[x], AppendTo[a, n]], {n, 0, 12^2}]; a (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *)


PROG

(PARI) isok(n) = (denominator(p=(5^n+1)/6) == 1) && isprime(p); \\ Michel Marcus, Oct 28 2017


CROSSREFS

Sequence in context: A059489 A197161 A059852 * A185230 A142009 A226412
Adjacent sequences: A057168 A057169 A057170 * A057172 A057173 A057174


KEYWORD

nonn,more


AUTHOR

N. J. A. Sloane, Sep 15 2000


EXTENSIONS

More terms from Kamil Duszenko (kdusz(AT)wp.pl), Jun 23 2003
30133 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008
a(10) discovered 10/29/08 is a probable prime based on trial factoring to 3.5e13 and Fermat testing base 2.  Paul Bourdelais, Nov 04 2008
a(11)=193939 from Paul Bourdelais discovered 12/24/08 is a probable prime based on trial factoring to 4e13 and Fermat primality testing base 2.  Paul Bourdelais, Dec 24 2008
a(12)=266863 is a probable prime discovered by Paul Bourdelais, Jul 09 2010
a(13)=277183 is a probable prime discovered by Paul Bourdelais, Jul 16 2010
a(14)=335429 is a probable prime discovered by Paul Bourdelais, Aug 23 2010


STATUS

approved



