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Numbers k such that (109*10^k + 17)/9 is prime.
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%I #14 May 18 2024 11:33:18

%S 2,3,9,23,27,32,50,80,107,140,992,1607,2975,4007,4605,12392,15159,

%T 16628,37419

%N Numbers k such that (109*10^k + 17)/9 is prime.

%C For k > 1, numbers k such that the digits 12 followed by k-1 occurrences of the digit 1 followed by the digit 3 is prime (see Example section).

%C a(20) > 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 121w3</a>.

%e 2 is in this sequence because (109*10^2 + 17)/9 = 1213 is prime.

%e Initial terms and associated primes:

%e a(1) = 2, 1213;

%e a(2) = 3, 12113;

%e a(3) = 9, 12111111113;

%e a(4) = 23, 1211111111111111111111113;

%e a(5) = 27, 12111111111111111111111111113; etc.

%t Select[Range[0, 100000], PrimeQ[(109*10^# + 17)/9] &]

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Nov 10 2017