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Numbers k such that (268*10^k - 1)/3 is prime.
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%I #10 May 26 2024 22:59:39

%S 0,2,6,7,12,13,17,18,26,77,151,222,403,567,1107,7221,7722,8475,9729,

%T 17904,21404,30170,62523

%N Numbers k such that (268*10^k - 1)/3 is prime.

%C Numbers k such that the digits 89 followed by k occurrences of the digit 3 is prime (see Example section).

%C a(24) > 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 893w</a>.

%e 2 is in this sequence because (268*10^2 - 1)/3 = 8933 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 89;

%e a(2) = 2, 8933;

%e a(3) = 6, 89333333;

%e a(4) = 7, 893333333;

%e a(5) = 12, 89333333333333; etc.

%t Select[Range[0, 100000], PrimeQ[(268*10^# - 1)/3] &]

%o (PARI) isok(k) = isprime((268*10^k - 1)/3); \\ _Altug Alkan_, Oct 11 2017

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Oct 11 2017