%I #31 Feb 01 2023 18:07:06

%S 1,65,85,89,101,385,623,7783,18535,113756,135878

%N Numbers k such that 70*R_k + 9 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

%C Also numbers k such that (7*10^(k+1)+11)/9 is prime.

%C a(12) > 2*10^5. - _Tyler Busby_, Feb 01 2023

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/7/77779.htm#prime">Prime numbers of the form 77...779</a>.

%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>

%F a(n) = A098089(n+1) - 1. - _Robert Price_, Nov 22 2014

%t Do[ If[ PrimeQ[70*(10^n - 1)/9 + 9], Print[n]], {n, 0, 5000}]

%t Select[Range[700], PrimeQ[(7 10^(# + 1) + 11) / 9] &] (* _Vincenzo Librandi_, Nov 22 2014 *)

%o (Magma) [n: n in [1..400] | IsPrime((7*10^(n+1)+11) div 9)]; _Vincenzo Librandi_, Nov 22 2014

%Y Cf. A002275, A093404, A098089.

%K hard,nonn

%O 1,2

%A _Robert G. Wilson v_, Aug 10 2000

%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

%E a(9) derived from A098089 by _Robert Price_, Nov 22 2014

%E a(10)-a(11) from _Tyler Busby_, Feb 01 2023