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Numbers k such that R_k + 9*10^k + 8 is prime, where R_k = 11...11 is the repunit (A002275) of length k.
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%I #13 Jul 08 2021 01:24:02

%S 0,2,246,1140,10394,43880

%N Numbers k such that R_k + 9*10^k + 8 is prime, where R_k = 11...11 is the repunit (A002275) of length k.

%C Also, numbers k such that (82*10^k + 71)/9 is prime.

%C Terms from Kamada data.

%C Note Kamada does not recognize k=0 as 17 is a degenerate case of form ABB..BBA.

%C a(7) > 10^5.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/abbba.htm">Near-repdigit numbers of the form ABB...BBA</a>.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/9/911119.htm#prime">Prime numbers of the form 911...119</a>.

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

%e For k=2, R_2 + 9*10^k + 8 = 11 + 900 + 8 = 919 which is prime.

%t Select[Range[0, 100000], PrimeQ[(82*10^#+71)/9] &]

%Y Cf. A002275.

%K more,hard,nonn

%O 1,2

%A _Robert Price_, Jun 18 2015