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]
H. Lifchitz, Mersenne and Fermat primes field
S. S. Wagstaff, Jr., The Cunningham Project
Eric Weisstein's World of Mathematics, Repunit
Index to primes in various ranges, form ((k+1)^n-1)/k
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
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