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%I #16 Sep 08 2022 08:46:12
%S 9,26,1268,14391
%N Numbers k such that R_(k+2) + 3*10^k is prime, where R_k = 11...1 is the repunit (A002275) of length k.
%C Also, numbers k such that (127*10^k - 1)/9 is prime.
%C Terms from Kamada.
%C a(5) > 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/1/14111.htm#prime">Prime numbers of the form 1411...11</a>.
%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.
%e For k=9, R_11 + 3*10^9 = 11111111111 + 3000000000 = 14111111111 which is prime.
%t Select[Range[0, 250000], PrimeQ[(127*10^#-1)/9 ] &]
%o (Magma) [n: n in [0..300] | IsPrime((127*10^n-1) div 9)]; // _Vincenzo Librandi_, Apr 14 2015
%o (PARI) for(n=0,400,if(isprime((127*10^n-1)/9),print1(n,", "))) \\ _Derek Orr_, Apr 14 2015
%Y Cf. A002275.
%K more,hard,nonn
%O 1,1
%A _Robert Price_, Apr 13 2015