A056664 Numbers k such that 80*R_k + 1 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

2, 18, 78, 138, 222, 462, 543, 1095, 1418, 3246, 3876, 4416, 9506, 11090, 14601, 27810, 29187

Offset: 1

Author

Robert G. Wilson v, Aug 09 2000

Keywords

• hard
• nonn

Comments

Also numbers k such that (8*10^(k+1) - 71)/9 is prime.

There are no other terms <= 2500. - Rick L. Shepherd, Mar 02 2004

a(18) > 10^5. - Robert Price, Nov 01 2014

Links

• Makoto Kamada, Prime numbers of the form 88...881.
• Index entries for primes involving repunits

Crossrefs

Cf. A002275, A092675 (corresponding primes), A099421.

Programs

Mathematica

Do[ If[ PrimeQ[ 80*(10^n - 1)/9 + 1 ], Print[n]], {n, 15000}]

Formula

a(n) = A099421(n+1) - 1. - Robert Price, Nov 01 2014

Extensions

a(9) (giving a probable prime) from Rick L. Shepherd, Mar 02 2004

a(10)-a(15) from N. J. A. Sloane, Feb 20 2005

a(16)-a(17) derived from A099421 by Robert Price, Nov 01 2014