%I #20 Jun 09 2024 22:16:20

%S 1,2,3,11,16,33,35,37,39,42,64,94,123,136,308,309,310,357,965,1109,

%T 2178,8916,9471,18330,62127,252209

%N Numbers k such that 7*10^k - 17 is prime.

%C For k > 1, numbers k such that the digit 6 followed by k-2 occurrences of the digit 9 followed by the digits 83 is prime (see Example section).

%C a(27) > 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 69w83</a>.

%e 3 is in this sequence because 7*10^3 - 17 = 6983 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 53;

%e a(2) = 2, 683;

%e a(3) = 3, 6983;

%e a(4) = 11, 699999999983;

%e a(5) = 16, 69999999999999983; etc.

%t Select[Range[1, 100000], PrimeQ[7*10^# - 17] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Jan 11 2017

%E Comment corrected by _Harvey P. Dale_, Apr 10 2019

%E a(26) from _Robert Price_, May 31 2023