login
Numbers k such that 10^k + 2*R_k + 7 is prime, where R_k = 11...1 is the repunit (A002275) of length k.
2

%I #28 Feb 01 2023 23:06:59

%S 1,3,6,51,57,63,150,393,420,547,42024,43063,101613,107385

%N Numbers k such that 10^k + 2*R_k + 7 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

%C Also numbers k such that (11*10^k + 61)/9 is prime.

%C a(13) > 10^5. - _Robert Price_, Jan 17 2015

%C a(15) > 2*10^5. - _Tyler Busby_, Feb 01 2023

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/1/12229.htm#prime">Prime numbers of the form 122...229</a>.

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

%F a(n) = A102011(n) + 1.

%t Do[ If[ PrimeQ[(11*10^n + 61)/9], Print[n]], {n, 0, 10000}]

%Y Cf. A002275, A102011.

%K more,nonn

%O 1,2

%A _Robert G. Wilson v_, Dec 16 2004

%E a(11)-a(12) from Erik Branger May 01 2013 by _Ray Chandler_, Aug 16 2013

%E a(13)-a(14) from _Tyler Busby_, Jan 31 2023