%I #11 May 19 2024 21:55:52
%S 1,5,7,14,17,40,53,95,97,113,122,125,145,374,470,485,1685,5324,8035,
%T 10745,52448,68059
%N Numbers k such that (62*10^k - 197)/9 is prime.
%C For k > 1, numbers k such that the digit 6 followed by k-2 occurrences of the digit 8 followed by the digits 67 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 68w67</a>.
%e 5 is in this sequence because (62*10^5 - 197)/9 = 6263 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 47;
%e a(2) = 5, 688867;
%e a(3) = 7, 68888867;
%e a(4) = 14, 688888888888867;
%e a(5) = 17, 688888888888888867; etc.
%t Select[Range[1, 100000], PrimeQ[(62*10^# - 197)/9] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Oct 29 2017