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Numbers k such that 8*10^k + 3*R_k is prime, where R_k = 11...1 is the repunit (A002275) of length k.
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%I #19 Jul 08 2021 05:05:48

%S 1,7,23,29,133,173,367,1925,3707,5765,9709,19573,43753

%N Numbers k such that 8*10^k + 3*R_k is prime, where R_k = 11...1 is the repunit (A002275) of length k.

%C Also numbers k such that (25*10^k - 1)/3 is prime.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/8/83333.htm#prime">Prime numbers of the form 833...33</a>.

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

%t Do[ If[ PrimeQ[ 8*10^n + 3*(10^n-1)/9], Print[n]], {n, 0, 10000}]

%Y Cf. A002275, A093676.

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Aug 11 2000

%E Corrected by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

%E 19573 and 43753 from Serge Batalov, Jan 2009 confirmed as next terms by _Ray Chandler_, Feb 13 2012