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

5, 7, 19, 31, 53, 67, 293, 641, 2137, 3011, 268207, 1600787

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• more

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.

Crossrefs

Equals 2*A054416 + 1.

Odd terms of A309358.

Programs

Mathematica

Select[Range[3000], PrimeQ[(10^# + 1) / 11] &] (* Vincenzo Librandi, Oct 29 2017 *)

PARI

isok(n) = (denominator(p=(10^n+1)/11)==1) && isprime(p); \\ Michel Marcus, Oct 29 2017

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