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Numbers k such that (5*10^k - 173)/3 is prime.
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%I #55 May 18 2024 11:32:58

%S 2,3,5,7,13,79,98,273,1173,3008,3118,4352,4748,5648,11167,11750,12555,

%T 26613,88303

%N Numbers k such that (5*10^k - 173)/3 is prime.

%C For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 6 followed by the digits 09 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 16w09</a>.

%e 2 is in this sequence because (5*10^2 - 173)/3 = 109 is prime.

%e Initial terms and associated primes:

%e a(1) = 2, 109;

%e a(2) = 3, 1609;

%e a(3) = 5, 166609;

%e a(4) = 7, 16666609;

%e a(5) = 13, 16666666666609; etc.

%t Select[Range[2, 100000], PrimeQ[(5*10^# - 173)/3] &]

%o (PARI) isok(k) = isprime((5*10^k - 173)/3); \\ _Michel Marcus_, Nov 12 2017

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Nov 11 2017