A056693 Numbers k such that 70*R_k + 9 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

1, 65, 85, 89, 101, 385, 623, 7783, 18535, 113756, 135878

Offset: 1

Author

Robert G. Wilson v, Aug 10 2000

Keywords

• hard
• nonn

Comments

Also numbers k such that (7*10^(k+1)+11)/9 is prime.

a(12) > 2*10^5. - Tyler Busby, Feb 01 2023

Links

• Makoto Kamada, Prime numbers of the form 77...779.
• Index entries for primes involving repunits

Crossrefs

Cf. A002275, A093404, A098089.

Programs

Magma

[n: n in [1..400] |  IsPrime((7*10^(n+1)+11) div 9)];  Vincenzo Librandi, Nov 22 2014

Mathematica

Do[ If[ PrimeQ[70*(10^n - 1)/9 + 9], Print[n]], {n, 0, 5000}]
Select[Range[700], PrimeQ[(7 10^(# + 1) + 11) / 9] &] (* Vincenzo Librandi, Nov 22 2014 *)

Formula

a(n) = A098089(n+1) - 1. - Robert Price, Nov 22 2014

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

a(9) derived from A098089 by Robert Price, Nov 22 2014

a(10)-a(11) from Tyler Busby, Feb 01 2023