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%I #12 May 03 2024 07:45:13
%S 1,2,4,8,22,37,38,64,80,92,104,136,164,172,349,1492,2551,16375,58087,
%T 59149
%N Numbers k such that (404*10^k - 53)/9 is prime.
%C For k > 1, numbers k such that the digits 44 followed by k-1 occurrences of the digit 8 followed by the digit 3 is prime (see Example section).
%C a(21) > 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 448w3</a>.
%e 2 is in this sequence because (404*10^2 - 53)/9 = 4483 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 443;
%e a(2) = 2, 4483;
%e a(3) = 4, 448883;
%e a(4) = 8, 4488888883;
%e a(5) = 22, 448888888888888888888883; etc.
%t Select[Range[0, 100000], PrimeQ[(404*10^# - 53)/9] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Nov 24 2017