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%I #20 May 26 2024 22:59:10
%S 3,4,6,9,34,36,126,141,160,286,678,1236,3757,4681,4881,6360,6588,7056,
%T 7752,41925,43423,43503,47565,52608,55084,76069,199248
%N Numbers k such that (10^k - 19)/9 is prime.
%C For k > 1, numbers k such that k-2 occurrences of the digit 1 followed by the digits 09 is prime (see Example section).
%C a(28) > 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 1w09</a>.
%e 4 is in this sequence because (10^4 - 19)/9 = 1109 is prime.
%e Initial terms and associated primes:
%e a(1) = 3, 109;
%e a(2) = 4, 1109;
%e a(3) = 6, 111109;
%e a(4) = 9, 111111109;
%e a(5) = 34, 1111111111111111111111111111111109; etc.
%t Select[Range[2, 100000], PrimeQ[10^# - 19)/9] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,1
%A _Robert Price_, Oct 06 2017
%E a(27) from _Robert Price_, Jan 02 2018