A056677 Numbers k such that 20*R_k + 7 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

0, 2, 8, 14, 27, 63, 1167, 1694, 2361, 116619

Offset: 1

Author

Robert G. Wilson v, Aug 10 2000

Keywords

• hard
• nonn
• more

Comments

Also numbers k such that (2*10^(k+1)+43)/9 is prime.

Links

• Makoto Kamada, Prime numbers of the form 22...227.
• Index entries for primes involving repunits

Crossrefs

Cf. A002275, A093167, A099409.

Programs

Mathematica

Do[ If[ PrimeQ[20*(10^n - 1)/9 + 7], Print[n]], {n, 0, 5000}]
Flatten[Position[Table[FromDigits[PadLeft[{7},n,2]],{n,5000}], ?PrimeQ]]-1 (* _Harvey P. Dale, May 01 2012 *)
Select[Range[0, 2500], PrimeQ[20*(10^n - 1)/9 + 7]&] (* Mikk Heidemaa, Nov 28 2015 *)

Formula

a(n) = A099409(n+1) - 1. - Robert Price, Jan 30 2015

Extensions

a(10) from Kamada link entered by Michael S. Branicky, Jan 14 2023