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%I #13 May 26 2024 15:23:42
%S 1,4,5,6,7,12,23,34,160,719,725,2568,3095,3520,3582,3791,4198,5236,
%T 15445,26431,33120,36028
%N Numbers k such that (17*10^k + 43)/3 is prime.
%C For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 6 followed by the digits 81 is prime (see Example section).
%C a(23) > 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 56w81</a>.
%e 4 is in this sequence because (17*10^4 + 43)/3 = 56681 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 71;
%e a(2) = 4, 56681;
%e a(3) = 5, 566681;
%e a(4) = 6, 5666681;
%e a(5) = 7, 56666681; etc.
%t Select[Range[0, 100000], PrimeQ[(17*10^# + 43)/3] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Oct 25 2017