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Numbers n such that 5*10^n + 8*R_n + 1 is prime, where R_n = 11...1 is the repunit (A002275) of length n.
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%I #13 Jan 17 2019 13:44:07

%S 1,4,8,13,16,44,439,608,1201,2725,5210,59389,118216,198529

%N Numbers n such that 5*10^n + 8*R_n + 1 is prime, where R_n = 11...1 is the repunit (A002275) of length n.

%C Also numbers n such that (53*10^n+1)/9 is prime.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/5/58889.htm#prime">Prime numbers of the form 588...889</a>.

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

%F a(n) = A101589(n) + 1.

%t Do[ If[ PrimeQ[(53*10^n + 1)/9], Print[n]], {n, 0, 10000}]

%Y Cf. A002275, A101589.

%K more,nonn

%O 1,2

%A _Robert G. Wilson v_, Jan 18 2005

%E Addition of a(12)-a(14) from Kamada data by _Robert Price_, Dec 12 2010