%I #17 Sep 08 2022 08:46:12
%S 0,1,12,16,33,37,42,6643,35157,63202,125292,200746
%N Numbers k such that R_(k+2) + 8*10^k is prime, where R_k = 11...1 is the repunit (A002275) of length k.
%C Also, numbers k such that (172*10^k - 1)/9 is prime.
%C Terms from Kamada.
%C a(13) > 250000.
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/abaaa.htm">Near-repdigit numbers of the form ABAA...AA</a>.
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/1/19111.htm#prime">Prime numbers of the form 1911...11</a>.
%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.
%e For k=1, R_3 + 8*10^1 = 111 + 80 = 191 which is prime.
%t Select[Range[0, 250000], PrimeQ[(172*10^#-1)/9 ] &]
%o (Magma) [n: n in [0..300] | IsPrime((172*10^n-1) div 9)]; // _Vincenzo Librandi_, Apr 14 2015
%o (PARI) for(n=0,300,if(isprime((172*10^n-1)/9),print1(n,", "))) \\ _Derek Orr_, Apr 14 2015
%Y Cf. A002275.
%K more,hard,nonn
%O 1,3
%A _Robert Price_, Apr 13 2015