%I #12 May 26 2024 22:59:28
%S 1,3,5,7,13,18,45,73,165,174,298,502,563,901,1033,1164,1181,2040,4165,
%T 20389,23608,34542,88761
%N Numbers k such that (17*10^k - 41)/3 is prime.
%C For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 6 followed by the digits 53 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 56w53</a>.
%e 3 is in this sequence because (17*10^3 - 41)/3 = 5653 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 43;
%e a(2) = 3, 5653;
%e a(3) = 5, 566653;
%e a(4) = 7, 56666653;
%e a(5) = 13, 56666666666653; etc.
%t Select[Range[1, 100000], PrimeQ[(17*10^# - 41)/3] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Sep 04 2017