OFFSET
1,1
COMMENTS
The a(10) to a(11) gap represents the largest relative gap seen so far in searching repunits with bases between -12 and 12. On average, there should have been 4 more primes added to this sequence by a(11), instead of just 1. - Paul Bourdelais, Feb 11 2010
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, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
P. Bourdelais, A Generalized Repunit Conjecture, 2009.
J. Brillhart, Letter to N. J. A. Sloane, Aug 08 1970
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. [Annotated scanned copy]
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
S. S. Wagstaff, Jr., The Cunningham Project
Eric Weisstein's World of Mathematics, Repunit
R. G. Wilson, v, Letter to N. J. A. Sloane, circa 1991.
MATHEMATICA
Select[Range[3000], PrimeQ[(10^# + 1) / 11] &] (* Vincenzo Librandi, Oct 29 2017 *)
PROG
(PARI) isok(n) = (denominator(p=(10^n+1)/11)==1) && isprime(p); \\ Michel Marcus, Oct 29 2017
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
EXTENSIONS
a(11) corresponds to a probable prime discovered by Paul Bourdelais, Feb 11 2010
a(12) corresponds to a probable prime discovered by Paul Bourdelais, May 04 2020
STATUS
approved