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A004061 Numbers k such that (5^k - 1)/4 is prime.
(Formerly M2620)
38
3, 7, 11, 13, 47, 127, 149, 181, 619, 929, 3407, 10949, 13241, 13873, 16519, 201359, 396413, 1888279, 3300593 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
With the addition of the 19th prime in the sequence, the new best linear fit to the sequence has G=0.4723, which is slightly closer to the conjectured limit of G=0.56145948, A080130 (see link for Generalized Repunit Conjecture). [Paul Bourdelais, Apr 30 2018]
REFERENCES
J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and later supplements.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Paul Bourdelais, A Generalized Repunit Conjecture [From Paul Bourdelais, Jun 01 2010]
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930.
H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930. [Annotated scanned copy]
S. S. Wagstaff, Jr., The Cunningham Project
Eric Weisstein's World of Mathematics, Repunit
MATHEMATICA
lst={}; Do[If[PrimeQ[(5^n-1)/4], AppendTo[lst, n]], {n, 10^4}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 20 2008 *)
PROG
(PARI) forprime(p=2, 1e4, if(ispseudoprime(5^p\4), print1(p", "))) \\ Charles R Greathouse IV, Jul 15 2011
CROSSREFS
Cf. A080130.
Sequence in context: A059055 A243367 A145670 * A354904 A277009 A277019
KEYWORD
hard,nonn
AUTHOR
EXTENSIONS
a(13)-a(15) from Kamil Duszenko (kdusz(AT)wp.pl), Mar 25 2003
a(16) corresponds to a probable prime based on trial factoring to 4*10^13 and Fermat primality testing base 2. - Paul Bourdelais, Dec 11 2008
a(17) corresponds to a probable prime discovered by Paul Bourdelais, Jun 01 2010
a(18) corresponds to a probable prime discovered by Paul Bourdelais, Apr 30 2018
a(19) corresponds to a probable prime discovered by Ryan Propper, Jan 02 2022
STATUS
approved

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Last modified March 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)