%I #11 Jun 07 2024 23:59:15

%S 1,2,5,9,13,20,21,32,33,56,73,81,149,313,455,753,1013,1166,1304,1679,

%T 15758,15896,21801,41353,45421,131090,151007

%N Numbers k such that (5*10^k + 37)/3 is prime.

%C For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 6 followed by the digits 79 is prime (see Example section).

%C a(28) > 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 16w79</a>.

%e 2 is in this sequence because (5*10^2 + 37) / 3 = 179 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 29;

%e a(2) = 2, 179;

%e a(3) = 5, 166679;

%e a(4) = 9, 1666666679;

%e a(5) = 13, 16666666666679; etc.

%t Select[Range[0, 100000], PrimeQ[(5*10^# + 37) / 3] &]

%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Jan 16 2017

%E a(26)-a(27) from _Robert Price_, Mar 02 2018