A056685 Numbers k such that 50*R_k + 3 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

0, 1, 7, 25, 65, 73, 232, 472, 539, 2773, 64714

Offset: 1

Author

Robert G. Wilson v, Aug 10 2000

Keywords

• hard
• nonn

Comments

Also numbers k such that (5*10^(k+1)-23)/9 is prime.

a(12) > 10^5. - Robert Price, Nov 13 2014

Links

• Makoto Kamada, Prime numbers of the form 55...553.
• Index entries for primes involving repunits

Crossrefs

Cf. A002275, A099416.

Programs

Magma

[n: n in [0..400]| IsPrime((5*10^(n+1)-23)div 9)]; // Vincenzo Librandi, Nov 14 2014

Mathematica

Do[ If[ PrimeQ[50*(10^n - 1)/9 + 3], Print[n]], {n, 0, 5000}]
Select[Range[0, 3000], PrimeQ[(5 10^(# + 1) - 23) / 9] &] (* Vincenzo Librandi, Nov 14 2014 *)

Formula

a(n) = A099416(n) - 1. - Robert Price, Nov 13 2014 [adapted by Georg Fischer, Jan 04 2021]

Extensions

a(11) derived from A099416 by Robert Price, Nov 13 2014