|
%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,changed
%O 1,1
%A _Robert Price_, Apr 12 2015
%E a(18)-a(22) from Kamada data by _Tyler Busby_, Apr 20 2024
|
