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Numbers k such that 8*10^k - 79 is prime.
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%I #14 May 18 2024 13:38:16

%S 5,6,13,28,64,199,233,364,457,695,1259,1267,1339,1962,2887,3897,6547,

%T 7881,11629,13777,15229,17956,24497,48196

%N Numbers k such that 8*10^k - 79 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 21 is prime (see Example section).

%C a(25) > 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 79w21</a>.

%e 5 is in this sequence because 8*10^5 - 79 = 799921 is prime.

%e Initial terms and associated primes:

%e a(1) = 5, 799921;

%e a(2) = 6, 7999921;

%e a(3) = 13, 79999999999921;

%e a(4) = 28, 79999999999999999999999999921; etc.

%t Select[Range[1, 100000], PrimeQ[8*10^# - 79] &]

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Nov 02 2017