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%I #26 Sep 08 2022 08:46:12
%S 1,2,3,9,10,13,19,25,33,124,150,175,199,290,301,506,592,1016,1459,
%T 4150,6396,7059,8311,8355,8811,13200,13270,26775,33303,62073,66043,
%U 154869,162153,172862
%N Numbers k such that 3*R_(k+2) + 5*10^k is prime, where R_k = 11...1 is the repunit (A002275) of length k.
%C Also, numbers k such that (115*10^k - 1)/3 is prime.
%C Terms from Kamada.
%C a(35) > 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/3/38333.htm#prime">Prime numbers of the form 3833...33</a>.
%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.
%e For k=2, 3*R_4 + 5*10^2 = 3333 + 500 = 3833 which is prime.
%t Select[Range[0, 250000], PrimeQ[(115*10^#-1)/3 ] &]
%o (PARI) for(n=0,300,if(isprime((115*10^n-1)/3),print1(n,", "))) \\ _Derek Orr_, Apr 14 2015
%o (Magma) [n: n in [0..300] | IsPrime((115*10^n-1) div 3)]; // _Vincenzo Librandi_, Apr 15 2015
%Y Cf. A002275.
%K more,hard,nonn
%O 1,2
%A _Robert Price_, Apr 14 2015
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