A098089 Numbers k such that 7*R_k + 2 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

0, 2, 66, 86, 90, 102, 386, 624, 7784, 18536, 113757, 135879

Offset: 1

Author

Julien Peter Benney (jpbenney(AT)ftml.net), Sep 14 2004

Keywords

• more
• nonn
• hard

Comments

Also numbers k such that (7*10^k + 11)/9 is prime.

Although perhaps a degenerate case, A002275 defines R(0)=0. Thus zero belongs in this sequence since 7*0 + 2 = 2 is prime. - Robert Price, Oct 28 2014

a(11) > 10^5. - Robert Price, Nov 22 2014

a(13) > 2*10^5. - Tyler Busby, Feb 01 2023

Examples

			If k = 2, we get (7*10^2 + 11)/9 = (700+11)/9 = 79, which is prime.
		

Links

• Makoto Kamada, Prime numbers of the form 77...779.
• Index entries for primes involving repunits

Crossrefs

Cf. A002275, A056693, A093404.

Programs

Magma

[n: n in [0..300] |  IsPrime((7*10^n+11) div 9)]; // Vincenzo Librandi, Nov 22 2014

Mathematica

Do[ If[ PrimeQ[ 7(10^n - 1)/9 + 2], Print[n]], {n, 0, 5000}] (* Robert G. Wilson v, Oct 15 2004 *)
Do[ If[ PrimeQ[((7*10^n) + 11)/9], Print[n]], {n, 0, 8131}] (* Robert G. Wilson v, Sep 27 2004 *)
Select[Range[0, 700], PrimeQ[(7 10^# + 11) / 9] &] (* Vincenzo Librandi, Nov 22 2014 *)

Formula

a(n) = A056693(n-1) + 1 for n>1.

Extensions

a(9) from Kamada link by Ray Chandler, Dec 23 2010

a(1)=0 added and Mathematica programs adapted by Robert Price, Oct 28 2014

a(11)-a(12) from Tyler Busby, Feb 01 2023