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

1,3

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

Table of n, a(n) for n=1..22.

Makoto Kamada, Prime numbers of the form 11...117.

Index entries for primes involving repunits

Formula

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

Mathematica

Do[ m = n; If[ primeQ[ 10*(10^n - 1)/9 + 7 ], Print[ n ] ], {n, 1, 1250} ]

Crossrefs

Cf. A093139 (corresponding primes), A097684.

Sequence in context: A338452 A030724 A124082 * A341810 A338511 A332971

Adjacent sequences: A056652 A056653 A056654 * A056656 A056657 A056658

Keyword

hard,nonn

Author

Robert G. Wilson v, Aug 09 2000

Extensions

2152 (giving a probable prime) from Rick L. Shepherd, Mar 23 2004

2575 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

Status

approved