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%I #29 Sep 08 2022 08:46:12
%S 0,2,3,9,11,18,74,131,144,161,224,282,390,398,614,791,1313,1866,9708,
%T 10544,13292,13394,29703,30779,72446
%N Numbers k such that 7*R_(k+2) - 6*10^k is prime, where R_k = 11...1 is the repunit (A002275) of length k.
%C Also, numbers k such that (646*10^k - 7)/9 is prime.
%C Terms from Kamada.
%C a(26) > 10^5. _Robert Price_, Jul 31 2016
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/">Factorization of near-repdigit-related numbers</a>.
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/primedifficulty.txt">Search for 717w</a>.
%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.
%e For k=2, 7*R_4 - 6*10^2 = 7777 - 600 = 7177 which is prime.
%e a(1) =0 associated with 71. a(2)=2 associated with 7177. a(3)=3 associated with 71777. a(4) = 9 associated with 71777777777 etc . - _Robert Price_, Jul 31 2016
%t Select[Range[0, 100000], PrimeQ[(646*10^#-7)/9 ] &]
%o (PARI) for(n=0,200,if(isprime((646*10^n-7)/9),print1(n,", "))) \\ _Derek Orr_, Apr 14 2015
%o (Magma) [n: n in [0..300] | IsPrime((646*10^n-7) div 9)]; // _Vincenzo Librandi_, Apr 15 2015
%Y Cf. A002275, A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K more,hard,nonn
%O 1,2
%A _Robert Price_, Apr 14 2015
%E a(25) from _Robert Price_, Jul 31 2016
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