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Numbers k such that (88*10^k - 1)/3 is prime.
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%I #12 Jun 02 2024 09:29:11

%S 0,1,3,6,9,121,153,172,378,496,841,1594,1924,2692,4617,5148,12891,

%T 24259,24684,27690,68256,93760,104989

%N Numbers k such that (88*10^k - 1)/3 is prime.

%C Numbers k such that the digits 29 followed by k occurrences of the digit 3 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 293w</a>.

%e 3 is in this sequence because (88*10^3 - 1)/3 = 29333 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 29;

%e a(2) = 1, 293;

%e a(3) = 3, 29333;

%e a(4) = 6, 29333333;

%e a(5) = 9, 29333333333; etc.

%t Select[Range[0, 100000], PrimeQ[(88*10^# - 1)/3] &]

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

%K nonn,more,hard

%O 1,3

%A _Robert Price_, Oct 11 2017

%E a(23) from _Robert Price_, Apr 05 2020