%I #12 May 19 2024 21:55:48

%S 1,2,3,14,95,123,135,144,155,221,239,324,462,830,3462,4124,9195,9767,

%T 24956,26744,98111,185529

%N Numbers k such that 8*10^k - 67 is prime.

%C For k > 1, numbers k such that the digit 7 followed by k-2 occurrences of the digit 9 followed by the digits 33 is prime (see Example section).

%C a(23) > 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 79w33</a>.

%e 2 is in this sequence because 8*10^2 - 67 = 733 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 13;

%e a(2) = 2, 733;

%e a(3) = 3, 7933;

%e a(4) = 14, 799999999999933; etc.

%t Select[Range[1, 100000], PrimeQ[8*10^# - 67] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Oct 29 2017

%E a(22) from _Robert Price_, Aug 05 2019