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A290962 Numbers k such that (13*10^k - 43)/3 is prime.

%I A290962 #19 May 27 2024 07:16:30
%S A290962 1,2,4,5,8,12,55,125,136,221,224,668,1254,2639,4745,5888,8526,9139,
%T A290962 13771,17936,27713,38668,44680,73891,135184,200610,215592,247793,
%U A290962 258710,291721
%N A290962 Numbers k such that (13*10^k - 43)/3 is prime.
%C A290962 For k > 1, numbers k 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 A290962 a(31) > 3*10^5.
%H A290962 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A290962 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 43w19</a>.
%e A290962 2 is in this sequence because (13*10^2 - 43)/3 = 419 is prime.
%e A290962 Initial terms and associated primes:
%e A290962 a(1) = 1, 29;
%e A290962 a(2) = 2, 419;
%e A290962 a(3) = 4, 43319;
%e A290962 a(4) = 5; 433319;
%e A290962 a(5) = 8, 433333319; etc.
%t A290962 Select[Range[1, 100000], PrimeQ[(13*10^# - 43)/3] &]
%o A290962 (PARI) isok(n) = ispseudoprime((13*10^n - 43)/3) \\ _Altug Alkan_, Aug 15 2017
%Y A290962 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A290962 nonn,more,hard
%O A290962 1,2
%A A290962 _Robert Price_, Aug 15 2017
%E A290962 a(25) from _Robert Price_, Nov 28 2018
%E A290962 a(26)-a(30) from _Robert Price_, Oct 26 2023