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Numbers k such that 10^k + 3*R_k + 6 is prime, where R_k = 11...1 is the repunit (A002275) of length k.
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%I #22 Feb 01 2023 19:49:31

%S 1,2,4,7,10,13,14,22,23,29,38,50,53,67,104,350,376,412,1205,1835,2510,

%T 2668,6097,8296,14296,43369,127349,142034

%N Numbers k such that 10^k + 3*R_k + 6 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

%C Also numbers k such that (4*10^k + 17)/3 is prime.

%C a(29) > 2*10^5. - _Tyler Busby_, Feb 01 2023

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/1/13339.htm#prime">Prime numbers of the form 133...339</a>.

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

%F a(n) = A102014(n) + 1.

%t Do[ If[ PrimeQ[(4*10^n + 17)/3], Print[n]], {n, 0, 10000}]

%Y Cf. A002275, A102014.

%K more,nonn

%O 1,2

%A _Robert G. Wilson v_, Dec 16 2004

%E Addition of a(25) from Kamada data by _Robert Price_, Dec 08 2010

%E a(26) from Erik Branger May 01 2013 by _Ray Chandler_, Aug 16 2013

%E a(27)-a(28) from _Tyler Busby_, Feb 01 2023