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

%I #27 Feb 01 2023 22:27:43

%S 0,1,3,9,48,58,153,261,876,1179,1596,17715,63718

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

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

%C a(14) > 10^5. - _Robert Price_, Nov 15 2014

%C a(14) > 2*10^5. - _Tyler Busby_, Feb 01 2023

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/1/12223.htm#prime">Prime numbers of the form 122...223</a>.

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

%F a(n) = A102009(n-1) + 1.

%t Do[ If[ PrimeQ[(11*10^n + 7)/9], Print[n]], {n, 0, 10000}]

%Y Cf. A002275, A102009.

%K more,nonn

%O 1,3

%A _Robert G. Wilson v_, Dec 16 2004

%E Addition of a(12) from Kamada data by _Robert Price_, Dec 13 2010

%E Inserted a(1)=0 by _Robert Price_, Nov 15 2014

%E a(13) from Kamada data by _Robert Price_, Nov 15 2014