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Numbers k such that (74*10^k + 133)/9 is prime.
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%I #14 Jun 08 2024 15:59:14

%S 0,1,3,4,7,10,19,24,27,85,93,99,133,292,309,676,894,2076,2236,10968,

%T 20628,29521,49054,57763,139723,150616

%N Numbers k such that (74*10^k + 133)/9 is prime.

%C For k > 1, numbers k such that the digit 8 followed by k-2 occurrences of the digit 2 followed by the digits 37 is prime (see Example section).

%C a(27) > 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 82w37</a>.

%e 3 is in this sequence because (74*10^3 + 133)/9 = 8237 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 23;

%e a(2) = 1, 97;

%e a(3) = 3, 8237;

%e a(4) = 4, 82237;

%e a(5) = 7, 82222237; etc.

%t Select[Range[0, 100000], PrimeQ[(74*10^# + 133)/9] &]

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

%K nonn,more,hard

%O 1,3

%A _Robert Price_, Oct 04 2017

%E a(25)-a(26) from _Robert Price_, Jun 21 2019