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Numbers k such that (62*10^k - 197)/9 is prime.
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%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