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Numbers k such that 5*10^k + 2*R_k + 5 is prime, where R_k = 11...1 is the repunit (A002275) of length k.
1

%I #22 Jan 17 2019 13:44:07

%S 3,5,33,48,59,60,74,126,177,228,638,1304,1644,2435,4374,8750,15114,

%T 16853,30353,30545,36236

%N Numbers k such that 5*10^k + 2*R_k + 5 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

%C Also numbers k such that (47*10^k + 43)/9 is prime.

%C a(22) > 10^5. - _Robert Price_, Jul 10 2015

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/5/52227.htm#prime">Prime numbers of the form 522...227</a>.

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

%F a(n) = A101575(n) + 1.

%t Do[ If[ PrimeQ[(46*10^n + 43)/9], Print[n]], {n, 0, 10000}]

%Y Cf. A002275, A101575.

%K more,nonn

%O 1,1

%A _Robert G. Wilson v_, Jan 18 2005

%E a(17)-a(18) from Kamada data by _Robert Price_, Dec 14 2010

%E a(19)-a(21) from Erik Branger May 01 2013 by _Ray Chandler_, Aug 16 2013