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%I #11 Jun 03 2024 23:31:12
%S 1,2,3,4,5,8,42,52,81,96,98,152,190,261,686,1930,2152,5694,6341,14067,
%T 18124,31678,58521,73647,128244
%N Numbers k such that (4*10^k - 19)/3 is prime.
%C For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 3 followed by the digits 27 is prime (see Example section).
%C a(26) > 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 13w27</a>.
%e 3 is in this sequence because (4*10^3 - 19)/3 = 1327 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 7;
%e a(2) = 2, 127;
%e a(3) = 3, 1327;
%e a(4) = 4, 13327;
%e a(5) = 5, 133327; etc.
%t Select[Range[1, 100000], PrimeQ[(4*10^# - 19)/3] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Jun 23 2017
%E a(25) from _Robert Price_, Mar 01 2018