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A271548 Numbers k such that 4*10^k + 19 is prime.

%I A271548 #17 Jun 06 2024 23:23:57
%S A271548 0,1,2,3,9,11,19,27,31,36,42,69,86,98,152,205,533,587,1302,1506,1521,
%T A271548 1573,1807,3906,6461,9081,11766,12595,15697,17154,30507,36074,52667,
%U A271548 61367,122377,169759
%N A271548 Numbers k such that 4*10^k + 19 is prime.
%C A271548 For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 0 followed by the digits 19 is prime (see Example section).
%C A271548 a(37) > 3*10^5.
%H A271548 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A271548 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 40w19</a>.
%e A271548 3 is in this sequence because 4*10^3 + 19 = 4019 is prime.
%e A271548 Initial terms and associated primes:
%e A271548 a(1) = 0, 23;
%e A271548 a(2) = 1, 59;
%e A271548 a(3) = 2, 419;
%e A271548 a(4) = 3, 4019;
%e A271548 a(5) = 9, 4000000019, etc.
%t A271548 Select[Range[0, 100000], PrimeQ[4*10^# + 19] &]
%o A271548 (PARI) is(n)=ispseudoprime(4*10^n + 19) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y A271548 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A271548 nonn,more
%O A271548 1,3
%A A271548 _Robert Price_, Apr 09 2016
%E A271548 a(35)-a(36) from _Robert Price_, Oct 22 2018