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A293531 Numbers k such that (268*10^k - 1)/3 is prime.

%I A293531 #10 May 26 2024 22:59:39
%S A293531 0,2,6,7,12,13,17,18,26,77,151,222,403,567,1107,7221,7722,8475,9729,
%T A293531 17904,21404,30170,62523
%N A293531 Numbers k such that (268*10^k - 1)/3 is prime.
%C A293531 Numbers k such that the digits 89 followed by k occurrences of the digit 3 is prime (see Example section).
%C A293531 a(24) > 10^5.
%H A293531 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A293531 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 893w</a>.
%e A293531 2 is in this sequence because (268*10^2 - 1)/3 = 8933 is prime.
%e A293531 Initial terms and associated primes:
%e A293531 a(1) = 0, 89;
%e A293531 a(2) = 2, 8933;
%e A293531 a(3) = 6, 89333333;
%e A293531 a(4) = 7, 893333333;
%e A293531 a(5) = 12, 89333333333333; etc.
%t A293531 Select[Range[0, 100000], PrimeQ[(268*10^# - 1)/3] &]
%o A293531 (PARI) isok(k) = isprime((268*10^k - 1)/3); \\ _Altug Alkan_, Oct 11 2017
%Y A293531 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A293531 nonn,more,hard
%O A293531 1,2
%A A293531 _Robert Price_, Oct 11 2017