%I #12 Jun 09 2024 18:05:28

%S 2,3,8,12,24,105,140,231,234,260,294,354,602,813,1562,2961,3450,5622,

%T 8121,9014,23052,38505,41139,63576

%N Numbers k such that (107*10^k - 17)/9 is prime.

%C For k > 0, numbers k such that the digits 11 followed by k-1 occurrences of the digit 8 followed by the digit 7 is prime (see Example section).

%C a(25) > 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 118w7</a>.

%e 3 is in this sequence because (107*10^3 - 17)/9 = 11887 is prime.

%e Initial terms and associated primes:

%e a(1) = 2, 1187;

%e a(2) = 3, 11887;

%e a(3) = 8, 1188888887;

%e a(4) = 12, 11888888888887;

%e a(5) = 24, 11888888888888888888888887; etc.

%t Select[Range[0, 100000], PrimeQ[(107*10^# - 17)/9] &]

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Feb 10 2017