%I #12 Jun 02 2024 14:05:08
%S 2,3,8,10,13,19,20,26,37,39,232,308,381,382,706,872,1707,1929,2195,
%T 9211,15567,58306
%N Numbers k such that (199*10^k + 11)/3 is prime.
%C For k > 0, numbers k such that the digits 66 followed by k-1 occurrences of the digit 3 followed by the digit 7 is prime (see Example section).
%C a(23) > 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 663w7</a>.
%e 3 is in this sequence because (199*10^3 + 11)/3 = 66337 is prime.
%e Initial terms and associated primes:
%e a(1) = 2, 6637;
%e a(2) = 3, 66337;
%e a(3) = 8, 6633333337;
%e a(4) = 10, 663333333337;
%e a(5) = 13, 663333333333337; etc.
%t Select[Range[0, 100000], PrimeQ[(199*10^# + 11)/3] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,1
%A _Robert Price_, May 01 2017