A097683 Numbers k such that R_k + 2 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

0, 1, 2, 3, 5, 9, 11, 24, 84, 221, 1314, 2952, 20016, 51054

Offset: 1

Author

Carl R. White and Julien Peter Benney (jpbenney(AT)ftml.net), Aug 19 2004

Keywords

• more
• nonn

Comments

Also numbers k such that (10^k + 17)/9 is prime.

The corresponding values R_k + 2 are primes of the form "(n-1) ones followed by a three"; zero is a degenerate case. Related to the base-10 repunit primes.

a(15) > 10^5. - Robert Price, Oct 12 2014

By Kamada link, a(15) > 4*10^5. - Jeppe Stig Nielsen, Jan 17 2023

Examples

			11113 = ((10^5)+17)/9 and 11113 is prime.
		

Links

• Makoto Kamada, Prime numbers of the form 11...113.
• Henri Lifchitz and Renaud Lifchitz, PRP Top, Search output for (10^k+17)/9
• Index entries for primes involving repunits

Crossrefs

Cf. A002275, A004023, A056654, A097684, A097685.

Programs

Maple

A097683:=n->`if`((10^n+17 mod 9) = 0 and isprime(floor((10^n+17)/9)),n,NULL): seq(A097683(n), n=0..10^3); # Wesley Ivan Hurt, Oct 12 2014

Mathematica

Do[ If[ PrimeQ[(10^n - 1)/9 + 2], Print[n]], {n, 0, 5951}] (* Robert G. Wilson v, Oct 15 2004 *)

Formula

a(n) = A056654(n-1) + 1.

Extensions

a(11)-a(12) from Robert G. Wilson v, Oct 15 2004

Edited by N. J. A. Sloane, Apr 02 2009, at the suggestion of Farideh Firoozbakht

a(13) from Kamada link by Ray Chandler, Dec 23 2010

a(14) from Robert Price, Oct 12 2014