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Numbers k such that (17*10^k - 41)/3 is prime.
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%I #12 May 26 2024 22:59:28

%S 1,3,5,7,13,18,45,73,165,174,298,502,563,901,1033,1164,1181,2040,4165,

%T 20389,23608,34542,88761

%N Numbers k such that (17*10^k - 41)/3 is prime.

%C For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 6 followed by the digits 53 is prime (see Example section).

%C a(24) > 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 56w53</a>.

%e 3 is in this sequence because (17*10^3 - 41)/3 = 5653 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 43;

%e a(2) = 3, 5653;

%e a(3) = 5, 566653;

%e a(4) = 7, 56666653;

%e a(5) = 13, 56666666666653; etc.

%t Select[Range[1, 100000], PrimeQ[(17*10^# - 41)/3] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Sep 04 2017