%I #15 Jul 25 2024 14:26:35

%S 1,2,3,9,17,18,20,24,29,36,48,114,126,135,153,170,241,363,483,579,681,

%T 948,2483,2798,3081,5137,5640,6890,7080,12600,16929,24253,24793,35546,

%U 52956,69645,133831,206688

%N Numbers k such that (11*10^k + 19)/3 is prime.

%C For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 6 followed by the digits 73 is prime (see Example section).

%C a(39) > 3*10^5.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 36w73</a>.

%e 3 is in this sequence because (11*10^3 + 19)/3 = 3673 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 43;

%e a(2) = 2, 373;

%e a(3) = 3, 3673;

%e a(4) = 9, 3666666673;

%e a(5) = 17, 366666666666666673, etc.

%t Select[Range[0, 100000], PrimeQ[(11*10^# + 19)/3] &]

%o (PARI) is(n)=isprime((11*10^n + 19)/3) \\ _Charles R Greathouse IV_, Mar 16 2016

%Y Cf. A056654, A268448, A269303.

%K nonn,more

%O 1,2

%A _Robert Price_, Mar 15 2016

%E a(37) from _Robert Price_, Sep 16 2018

%E a(38) from _Robert Price_, Jul 25 2024