%I #27 Jun 08 2024 08:55:32
%S 4,5,10,13,16,106,130,148,880,1261,2560,2629,3730,5284,7411,8255,9091,
%T 9490,10171,14033,25618,39382,47452
%N Numbers k such that (17*10^k - 179)/9 is prime.
%C For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 8 followed by the digits 69 is prime (see Example section).
%C a(24) > 2*10^5.
%H Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 18w69</a>.
%e 5 is in this sequence because (17*10^5 - 179)/9 = 188869 is prime.
%e Initial terms and associated primes:
%e a(1) = 4, 18869;
%e a(2) = 5, 188869;
%e a(3) = 10, 18888888869;
%e a(4) = 13, 18888888888869;
%e a(5) = 16, 18888888888888869; etc.
%t Select[Range[2, 100000], PrimeQ[(17*10^# - 179)/9] &]
%o (PARI) is(n)=isprime((17*10^k - 179)/9) \\ _Charles R Greathouse IV_, Mar 05 2017
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,1
%A _Robert Price_, Mar 05 2017