A056655 Numbers k such that 10*R_k + 7 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

0, 1, 3, 4, 7, 22, 28, 39, 130, 135, 214, 610, 766, 2152, 2575, 22972, 42688, 85711, 85863, 112066, 538507, 631714

Offset: 1

Author

Robert G. Wilson v, Aug 09 2000

Keywords

• hard
• nonn
• more

Comments

Also numbers k such that (10^(k+1)+53)/9 is prime.

2575 also produces a probable prime.

a(20) > 10^5. - Robert Price, Jan 13 2015

a(23) > 670000 (per the Kamada link). - Bill McEachen, Mar 02 2024

Links

• Makoto Kamada, Prime numbers of the form 11...117.
• Index entries for primes involving repunits

Crossrefs

Cf. A093139 (corresponding primes), A097684.

Programs

Mathematica

Do[ If[ PrimeQ[ 10*(10^n - 1)/9 + 7 ], Print[ n ] ], {n, 0, 1250} ]

Formula

a(n) = A097684(n) - 1 for all n >= 0. - Rick L. Shepherd, Aug 23 2004

Extensions

a(14) (giving a probable prime) from Rick L. Shepherd, Mar 23 2004

a(15) from Rick L. Shepherd, Aug 23 2004

a(16)-a(19) derived from A097684 by Robert Price, Jan 13 2015

a(20)-a(22) from the Kamada link by Bill McEachen, Mar 02 2024