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Numbers k such that 8*10^k - 99 is prime.
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%I #22 Jun 09 2024 18:06:28

%S 2,3,4,9,22,50,67,82,87,89,130,134,170,179,220,832,1425,1648,2356,

%T 2434,6556,11391,12610,20278,46509,50253

%N Numbers k such that 8*10^k - 99 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 01 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 79w01</a>.

%e 3 is in this sequence because 8*10^3-99 = 7901 is prime.

%e Initial terms and associated primes:

%e a(1) = 2, 701;

%e a(2) = 3, 7901;

%e a(3) = 4, 79901;

%e a(4) = 9, 7999999901;

%e a(5) = 22, 79999999999999999999901; etc.

%t Select[Range[2, 100000], PrimeQ[8*10^#-99] &]

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Feb 21 2017