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%I #11 May 25 2024 19:39:07
%S 2,3,6,12,24,31,33,45,66,109,150,187,345,1000,1026,1189,1959,2754,
%T 3405,5047,16291,29958,41547,41709,48908,72274,100257,103981
%N Numbers k such that 4*10^k - 83 is prime.
%C For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 9 followed by the digits 17 is prime (see Example section).
%C a(29) > 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 39w17</a>.
%e 3 is in this sequence because 4*10^3 - 83 = 3917 is prime.
%e Initial terms and associated primes:
%e a(1) = 2, 317;
%e a(2) = 3, 3917;
%e a(3) = 6, 3999917;
%e a(4) = 12, 3999999999917;
%e a(5) = 24, 3999999999999999999999917; etc.
%t Select[Range[2, 100000], PrimeQ[4*10^# - 83] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,1
%A _Robert Price_, Oct 23 2017
%E a(27)-a(28) from _Robert Price_, Oct 04 2018
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