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Numbers n such that 6*10^n + 5*R_n + 2 is prime, where R_n = 11...1 is the repunit (A002275) of length n.
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%I #14 Jan 17 2019 13:44:07

%S 1,4,9,21,48,84,696,1489,4167,8400,52099

%N Numbers n such that 6*10^n + 5*R_n + 2 is prime, where R_n = 11...1 is the repunit (A002275) of length n.

%C Also numbers n such that (59*10^n+13)/9 is prime.

%C a(12) > 10^5. - _Robert Price_, Sep 20 2015

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/6/65557.htm#prime">Prime numbers of the form 655...557</a>.

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

%F a(n) = A101533(n) + 1.

%t Do[ If[ PrimeQ[(59*10^n + 13)/9], Print[n]], {n, 0, 10000}]

%Y Cf. A002275, A101533.

%K more,nonn

%O 1,2

%A _Robert G. Wilson v_, Jan 18 2005

%E a(11) from _Robert Price_, Sep 20 2015