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%I #16 Oct 26 2023 11:37:11
%S 1,2,4,6,14,15,24,48,78,112,122,334,504,872,914,1230,1506,2442,4095,
%T 5022,10615,11460,18303,33675,47701,55592,84159,146661,269517,287085
%N Numbers k such that (22*10^k - 19)/3 is prime.
%C For k > 1, numbers such that the digit 7 followed by k - 2 occurrences of the digit 3 followed by the digits 27 is prime (see Example section).
%C a(31) > 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/primedifficulty.txt">Search for 73w27</a>.
%e 4 is in this sequence because (22*10^4 - 19)/3 = 73327 is prime.
%e Initial terms and primes associated:
%e a(1) = 1, 67;
%e a(2) = 2, 727;
%e a(3) = 4, 73327;
%e a(4) = 6, 7333327;
%e a(5) = 14, 733333333333327; etc.
%t Select[Range[0, 100000], PrimeQ[(22 * 10^# - 19)/3] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Feb 06 2017
%E a(28) from _Robert Price_, Apr 27 2019
%E a(29)-a(30) from _Robert Price_, Oct 26 2023
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