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%I #13 Jun 10 2024 08:43:35
%S 0,1,2,3,8,9,19,20,24,28,70,102,123,344,2228,3282,4554,5370,5830,
%T 12328,21742,27937,49261,89037
%N Numbers k such that (52*10^k - 1)/3 is prime.
%C For k > 1, numbers k such that the digits 17 followed by k occurrences of the digit 3 is prime (see Example section).
%C a(25) > 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 173w</a>.
%e 3 is in this sequence because (52*10^3 - 1)/3 = 17333 is prime.
%e Initial terms and associated primes:
%e a(1) = 0, 17;
%e a(2) = 1, 173;
%e a(3) = 2, 1733;
%e a(4) = 3, 17333;
%e a(5) = 8, 1733333333; etc.
%t Select[Range[0, 100000], PrimeQ[(52*10^# - 1)/3] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,3
%A _Robert Price_, Feb 16 2017