%I #17 May 25 2024 14:16:51

%S 1,2,3,4,5,7,9,15,27,29,39,62,77,106,114,357,555,962,1013,2372,8235,

%T 16047,82323,294308

%N Numbers k such that (11*10^k + 91)/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 97 is prime (see Example section).

%C a(25) > 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/prime_difficulty.txt">Search for 36w97</a>.

%e 3 is in this sequence because (11*10^3 + 91)/3 = 3697 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 67;

%e a(2) = 2, 397;

%e a(3) = 3, 3697;

%e a(4) = 4, 36697;

%e a(5) = 5, 366697; etc.

%t Select[Range[0, 100000], PrimeQ[(11*10^# + 91)/3] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Feb 24 2017

%E a(24) from _Robert Price_, Jul 12 2023