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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 (list; graph; refs; listen; history; text; internal format)
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.
H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
Eric Weisstein's World of Mathematics, Repunit
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
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

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Last modified July 18 16:59 EDT 2024. Contains 374388 sequences. (Running on oeis4.)