%I #21 May 26 2024 15:24:07
%S 1,3,6,12,16,18,27,30,59,60,61,118,198,208,826,1696,1813,4505,7111,
%T 9715,11572,15439,17406,55998,89836,158544,199801,201547
%N Numbers k such that (299*10^k - 17)/3 is prime.
%C For k > 1, numbers k such that the digits 99 followed by k-1 occurrences of the digit 6 followed by the digit 1 is prime (see Example section).
%C a(29) > 3*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 996w1</a>.
%e 3 is in this sequence because (299*10^3 - 17) / 3 = 99661 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 991;
%e a(2) = 3, 99661;
%e a(3) = 6, 99666661;
%e a(4) = 12, 99666666666661;
%e a(5) = 16, 996666666666666661; etc.
%t Select[Range[0, 100000], PrimeQ[(299*10^# - 17) / 3] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Jan 13 2017
%E a(26)-a(27) from _Robert Price_, Apr 15 2020
%E Constant 229 corrected to 299 by _Georg Fischer_, Jun 26 2020
%E a(28) from _Robert Price_, Jun 21 2023