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%I #12 Jun 10 2024 23:36:45
%S 3,6,11,14,20,38,55,206,1327,1676,1715,1814,2030,2406,2599,3251,4493,
%T 5066,6029,8745,24918,26672,70363,77556
%N Numbers k such that (23*10^k + 97)/3 is prime.
%C For k > 1, numbers k such that the digit 7 followed by k-2 occurrences of the digit 6 followed by the digits 99 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 76w99</a>.
%e 6 is in this sequence because (23*10^6 + 97)/3 = 7666699 is prime.
%e Initial terms and associated primes:
%e a(1) = 3, 7699;
%e a(2) = 6, 7666699;
%e a(3) = 11, 766666666699;
%e a(4) = 14, 766666666666699;
%e a(5) = 20, 766666666666666666699; etc.
%t Select[Range[0, 100000], PrimeQ[(23*10^# + 97)/3] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,1
%A _Robert Price_, Feb 10 2017