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%I #12 May 26 2024 22:59:45
%S 1,2,4,5,8,16,17,77,124,284,287,988,3277,4123,5290,12317,18280,18302,
%T 20266,20665,41420,56224,100997,174754
%N Numbers k such that (19*10^k + 737)/9 is prime.
%C For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 1 followed by the digits 93 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 21w93</a>.
%e 2 is in this sequence because (19*10^2 + 737)/9 = 293 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 103;
%e a(2) = 2, 293;
%e a(3) = 4, 21193;
%e a(4) = 5, 211193;
%e a(5) = 8, 211111193; etc.
%t Select[Range[0, 100000], PrimeQ[(19*10^# + 737)/9] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Oct 11 2017
%E a(23)-a(24) from _Robert Price_, Jul 13 2018
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