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Numbers k such that 2*10^k + 4*R_k - 1 is prime, where R_k = 11...1 is the repunit (A002275) of length k.
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%I #20 Jul 08 2021 01:35:19

%S 1,4,7,12,30,94,178,196,564,1801,3520,3538,8233,35161,37405,42330,

%T 70051,90792,124096,152670

%N Numbers k such that 2*10^k + 4*R_k - 1 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

%C Also numbers k such that (22*10^k - 13)/9 is prime.

%C a(21) > 2*10^5. - _Robert Price_, Jun 11 2018

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/2/24443.htm#prime">Prime numbers of the form 244...443</a>.

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

%F a(n) = A101958(n) + 1.

%t Do[ If[ PrimeQ[(22*10^n - 13)/9], Print[n]], {n, 0, 10000}]

%Y Cf. A002275, A101958.

%K more,nonn

%O 1,2

%A _Robert G. Wilson v_, Dec 17 2004

%E a(14)-a(16) from Erik Branger May 01 2013 by _Ray Chandler_, Aug 16 2013

%E a(17)-a(18) from _Robert Price_, Mar 16 2015

%E a(19)-a(20) from _Robert Price_, Jun 11 2018