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Numbers k such that (67*10^k + 17)/3 is prime.
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%I #11 Jun 10 2024 23:36:29

%S 1,2,4,8,11,20,21,32,33,41,93,187,265,380,1088,1459,1671,7328,11524,

%T 14167,21719,47439,74045

%N Numbers k such that (67*10^k + 17)/3 is prime.

%C For k > 1, numbers k such that the digits 22 followed by k-1 occurrences of the digit 3 followed by the digit 9 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 223w9</a>.

%e 4 is in this sequence because (67*10^4 + 17)/3 = 223339 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 229;

%e a(2) = 2, 2239;

%e a(3) = 4, 223339;

%e a(4) = 8, 2233333339;

%e a(5) = 11, 2233333333339; etc.

%t Select[Range[0, 100000], PrimeQ[(67*10^# + 17)/3] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Feb 19 2017