%I #19 Jun 02 2024 20:58:38

%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 k 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/prime_difficulty.txt">Search for 73w27</a>.

%e 4 is in this sequence because (22*10^4 - 19)/3 = 73327 is prime.

%e Initial terms and associated primes:

%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