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%I #15 Oct 26 2023 11:37:54
%S 1,2,4,5,8,12,55,125,136,221,224,668,1254,2639,4745,5888,8526,9139,
%T 13771,17936,27713,38668,44680,73891,135184,200610,215592,247793,
%U 258710,291721
%N Numbers k such that (13*10^k - 43)/3 is prime.
%C For k>1, numbers such that the digit 4 followed by k-2 occurrences of the digit 3 followed by the digits 19 is prime (see Example section).
%C a(31) > 3*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/primedifficulty.txt">Search for 43w19.</a>
%e 2 is in this sequence because (13*10^2 - 43)/3 = 419 is prime.
%e Initial terms and primes associated:
%e a(1) = 1, 29;
%e a(2) = 2, 419;
%e a(3) = 4, 43319;
%e a(4) = 5; 433319;
%e a(5) = 8, 433333319; etc.
%t Select[Range[1, 100000], PrimeQ[(13*10^# - 43)/3] &]
%o (PARI) isok(n) = ispseudoprime((13*10^n - 43)/3) \\ _Altug Alkan_, Aug 15 2017
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Aug 15 2017
%E a(25) from _Robert Price_, Nov 28 2018
%E a(26)-a(30) from _Robert Price_, Oct 26 2023
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