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%I #14 May 18 2024 11:34:00
%S 1,2,3,6,7,13,18,33,39,126,154,168,213,4150,4153,5658,6394,21993,
%T 29674,38936,47095,94096,135174,139398
%N Numbers k such that (10^k + 191)/3 is prime.
%C For k > 1, numbers k such that k-2 occurrences of the digit 3 followed by the digits 97 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 3w97</a>.
%e 2 is in this sequence because (10^2 + 191)/3 = 97 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 67;
%e a(2) = 2, 97;
%e a(3) = 3, 397;
%e a(4) = 6, 333397;
%e a(5) = 7, 3333397; etc.
%t Select[Range[0, 100000], PrimeQ[(10^# + 191)/3] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Nov 10 2017
%E a(23)-a(24) from _Robert Price_, Feb 14 2018