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Numbers k such that 7*R_k + 10 is prime, where R_k = 11...1 is the repunit (A002275) of length k.
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%I #14 Feb 01 2023 19:49:44

%S 1,3,6,15,21,24,31,291,408,457,643,2671,2676,10893,21151,26445,77304,

%T 96312

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

%C Also, numbers k such that (7*10^k + 83)/9 is prime.

%C Terms from Kamada. Note Kamada does not recognize k=1 as 17 is a degenerate case of form AAA..ABA.

%C a(17) > 30000.

%C a(19) > 2*10^5. - _Tyler Busby_, Feb 01 2023

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

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/7/77787.htm#prime">Prime numbers of the form 77...7787</a>.

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

%e For k=3, 7*R_11 + 10 = 777 + 10 = 787 which is prime.

%t Select[Range[0, 30000], PrimeQ[(7*10^# + 83)/9] &]

%Y Cf. A002275.

%K more,hard,nonn

%O 1,2

%A _Robert Price_, Apr 12 2015

%E a(17)-a(18) from _Tyler Busby_, Feb 01 2023