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Numbers n such that 9*10^n + 2*R_n + 1 is prime, where R_n = 11...1 is the repunit (A002275) of length n.
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%I #17 Jan 17 2019 13:44:07

%S 5,29,60,147,186,456,678,1373,3378,15726,68231

%N Numbers n such that 9*10^n + 2*R_n + 1 is prime, where R_n = 11...1 is the repunit (A002275) of length n.

%C Also numbers n such that (83*10^n+7)/9 is prime.

%C a(12) > 10^5. - _Robert Price_, Oct 31 2015

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/9/92223.htm#prime">Prime numbers of the form 922...223</a>.

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

%F a(n) = A101002(n) + 1.

%t Do[ If[ PrimeQ[(83*10^n + 7)/9], Print[n]], {n, 0, 10000}]

%Y Cf. A002275, A101002.

%K more,nonn

%O 1,1

%A _Robert G. Wilson v_, Jan 19 2005

%E a(10) from Kamada data by _Robert Price_, Dec 14 2010

%E a(11) from _Robert Price_, Oct 31 2015