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%I #14 Jun 08 2024 15:41:31
%S 3,5,6,9,11,53,105,125,137,228,789,1259,1661,1697,1785,3737,6054,7614,
%T 11819,27366,28320,48678,69321,76067,97085
%N Numbers k such that (41*10^k + 373)/9 is prime.
%C For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 5 followed by the digits 97 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 45w97</a>.
%e 5 is in this sequence because (41*10^5 + 373)/9 = 455597 is prime.
%e Initial terms and associated primes:
%e a(1) = 3, 4597;
%e a(2) = 5, 455597;
%e a(3) = 6, 4555597;
%e a(4) = 9, 4555555597;
%e a(5) = 11, 455555555597; etc.
%t Select[Range[0, 100000], PrimeQ[(41*10^# + 373)/9] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,1
%A _Robert Price_, Apr 17 2017
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