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Numbers k such that 7*10^k - 89 is prime.
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%I #11 Jun 09 2024 22:16:12

%S 3,4,6,7,12,13,23,28,42,51,66,247,291,623,3429,3892,4416,7366,7991,

%T 8737,10151,10209,40129,41604,50818,68088

%N Numbers k such that 7*10^k - 89 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 11 is prime (see Example section).

%C a(27) > 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 69w11</a>.

%e 4 is in this sequence because 7*10^4 - 89 = 69911 is prime.

%e Initial terms and associated primes:

%e a(1) = 3, 6911;

%e a(2) = 4, 69911;

%e a(3) = 6, 6999911;

%e a(4) = 7, 69999911;

%e a(5) = 12, 6999999999911; etc.

%t Select[Range[2, 100000], PrimeQ[7*10^# - 89] &]

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Jan 31 2017