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Numbers k such that (199*10^k + 11)/3 is prime.
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%I #12 Jun 02 2024 14:05:08

%S 2,3,8,10,13,19,20,26,37,39,232,308,381,382,706,872,1707,1929,2195,

%T 9211,15567,58306

%N Numbers k such that (199*10^k + 11)/3 is prime.

%C For k > 0, numbers k such that the digits 66 followed by k-1 occurrences of the digit 3 followed by the digit 7 is prime (see Example section).

%C a(23) > 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 663w7</a>.

%e 3 is in this sequence because (199*10^3 + 11)/3 = 66337 is prime.

%e Initial terms and associated primes:

%e a(1) = 2, 6637;

%e a(2) = 3, 66337;

%e a(3) = 8, 6633333337;

%e a(4) = 10, 663333333337;

%e a(5) = 13, 663333333333337; etc.

%t Select[Range[0, 100000], PrimeQ[(199*10^# + 11)/3] &]

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, May 01 2017