A001562 Numbers n such that (10^n + 1)/11 is a prime. (Formerly M3767 N1537)

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

Table of n, a(n) for n=1..12.

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

Equals 2*A054416 + 1.

Odd terms of A309358.

Sequence in context: A128335 A023246 A022889 * A163386 A200178 A064101

Adjacent sequences: A001559 A001560 A001561 * A001563 A001564 A001565

Keyword

nonn,hard,more

Author

N. J. A. Sloane

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