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Numbers k such that 2*R_k + 9*10^k + 7 is prime, where R_k = 11...11 is the repunit (A002275) of length k.
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%I #12 Sep 08 2022 08:46:13

%S 2,6,12,110,3608,37784

%N Numbers k such that 2*R_k + 9*10^k + 7 is prime, where R_k = 11...11 is the repunit (A002275) of length k.

%C Also, numbers k such that (83*10^k + 61)/9 is prime.

%C Terms from Kamada data.

%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/9/92229.htm#prime">Prime numbers of the form 922...229</a>.

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

%e For k=2, 2*R_2 + 9*10^k + 7 = 22 + 900 + 7 = 929 which is prime.

%t Select[Range[0, 100000], PrimeQ[(83*10^#+61)/9] &]

%o (Magma) [n: n in [0..300] | IsPrime((83*10^n+61) div 9)]; // _Vincenzo Librandi_, Jun 19 2015

%Y Cf. A002275.

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Jun 18 2015