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Numbers k such that 2*10^k + R_k + 8 is prime, where R_k = 11...1 is the repunit (A002275) of length k.
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%I #19 Jul 08 2021 01:35:30

%S 1,223,318,427,3727,5227,8779,11383,15415,26382

%N Numbers k such that 2*10^k + R_k + 8 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

%C Also numbers k such that (19*10^k + 71)/9 is prime.

%C a(11) > 10^5. - _Robert Price_, Feb 06 2015

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/2/21119.htm#prime">Prime numbers of the form 211...119</a>.

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

%F a(n) = A101955(n) + 1.

%t Do[ If[ PrimeQ[(19*10^n + 71)/9], Print[n]], {n, 0, 10000}]

%Y Cf. A002275, A101955.

%K more,nonn

%O 1,2

%A _Robert G. Wilson v_, Dec 17 2004

%E Addition of a(8)-a(10) from Kamada data by _Robert Price_, Dec 13 2010