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%I #22 Jun 10 2024 08:43:30
%S 1,2,3,4,5,6,7,21,22,101,111,132,174,201,265,335,388,537,1011,1012,
%T 1254,6766,20236,55833,104014,134786,146181,159921,210011
%N Numbers k such that (19*10^k - 49)/3 is prime.
%C For k > 1, numbers k such that the digit 6 followed by k-2 occurrences of the digit 3 followed by the digits 17 is prime (see Example section).
%C a(30) > 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 63w17</a>.
%e 3 is in this sequence because (19*10^3 - 49)/3 = 6317 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 47;
%e a(2) = 2, 617;
%e a(3) = 3, 6317;
%e a(4) = 4, 63317;
%e a(5) = 5, 633317; etc.
%t Select[Range[1, 100000], PrimeQ[(19*10^# - 49)/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(25)-a(28) from _Robert Price_, May 18 2019
%E a(29) from _Robert Price_, Jun 17 2023