A057171 Numbers n such that (5^n+1)/6 is a prime.

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

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

Table of n, a(n) for n=1..15.

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

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

Status

approved