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Numbers k such that 12*10^k - 7 is prime.
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%I #17 May 11 2024 19:23:43

%S 0,1,2,4,5,8,11,21,25,105,191,305,463,704,1320,1404,1580,1675,2215,

%T 3475,6323,10560,28817,30356,98198

%N Numbers k such that 12*10^k - 7 is prime.

%C For k > 1, numbers k such that the digits 11 followed by k-1 occurrences of the digit 9 followed by the digit 3 is prime (see Example section).

%C a(26) > 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 119w3</a>.

%e 2 is in this sequence because 12*10^2 - 7 = 1193 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 5;

%e a(2) = 1, 113;

%e a(3) = 2, 1193;

%e a(4) = 4, 119993;

%e a(5) = 5, 1199993; etc.

%t Select[Range[0, 100000], PrimeQ[12*10^# - 7 ] &]

%o (PARI) isok(k) = isprime(12*10^k - 7); \\ _Michel Marcus_, Nov 13 2017

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

%K nonn,more,hard

%O 1,3

%A _Robert Price_, Nov 12 2017