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Numbers k such that 7*R_(k+2) - 10^k is prime, where R_k = 11...1 is the repunit (A002275) of length k.
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%I #18 Sep 08 2022 08:46:12

%S 3,9,132,8547,13215,14110

%N Numbers k such that 7*R_(k+2) - 10^k is prime, where R_k = 11...1 is the repunit (A002275) of length k.

%C Also, numbers k such that (691*10^k-7)/9 is prime.

%C Terms from Kamada.

%C a(7) > 30000.

%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/7/76777.htm#prime">Prime numbers of the form 7677...77</a>.

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

%e For k=3, 7*R_5 - 10^3 = 77777 - 1000 = 76777 which is prime.

%t Select[Range[0, 30000], PrimeQ[(691*10^#-7)/9 ] &]

%o (Magma) [n: n in [0..400] | IsPrime((691*10^n-7) div 9)]; // _Vincenzo Librandi_, Apr 15 2015

%Y Cf. A002275.

%K more,hard,nonn

%O 1,1

%A _Robert Price_, Apr 14 2015