

A057171


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


35



5, 67, 101, 103, 229, 347, 4013, 23297, 30133, 177337, 193939, 266863, 277183, 335429, 1856147
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OFFSET

1,1


COMMENTS

With the discovery of a(15), the best fit line slope G=0.55167 (see link to Generalized Repunit Conjecture). This sequence is converging nicely to the conjectured slope G=0.56145948.  Paul Bourdelais, Feb 26 2019


LINKS

J. Brillhart et al., Factorizations of b^n + 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
Eric Weisstein's World of Mathematics, Repunit


MATHEMATICA



PROG

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


CROSSREFS



KEYWORD

nonn,more


AUTHOR



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
a(15)=1856147 corresponds to a probable prime discovered by Paul Bourdelais, Feb 26 2019


STATUS

approved



