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A001562
Numbers n such that (10^n + 1)/11 is a prime.
(Formerly M3767 N1537)
27
5, 7, 19, 31, 53, 67, 293, 641, 2137, 3011, 268207, 1600787
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 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.
S. S. Wagstaff, Jr., The Cunningham Project
Eric Weisstein's World of Mathematics, Repunit
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
Equals 2*A054416 + 1.
Odd terms of A309358.
Sequence in context: A128335 A023246 A022889 * A163386 A200178 A064101
KEYWORD
nonn,hard,more
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