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Numbers k such that 7*R_k + 20 is prime, where R_k = 11...1 is the repunit (A002275) of length k.
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%I #45 Apr 20 2024 02:46:18

%S 2,3,5,17,44,47,78,504,533,768,915,1155,1313,7128,8088,15717,33074,

%T 43568,58689,82517,85647,154211

%N Numbers k such that 7*R_k + 20 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

%C Also, numbers k such that (7*10^k + 173)/9 is prime.

%C Terms from Kamada.

%C a(23) > 200000. - _Tyler Busby_, Apr 20 2024

%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/7/77797.htm#prime">Prime numbers of the form 77...7797</a>.

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

%e For k=3, 7*R_11 + 20 = 777 + 20 = 797 which is prime.

%t Select[Range[0, 30000], PrimeQ[(7*10^# + 173)/9] &]

%o (Magma) [n: n in [0..400] | IsPrime((7*10^n + 173) div 9)]; // _Vincenzo Librandi_, Apr 13 2015

%Y Cf. A002275.

%K more,hard,nonn

%O 1,1

%A _Robert Price_, Apr 12 2015

%E a(18)-a(22) from Kamada data by _Tyler Busby_, Apr 20 2024