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%I #19 May 26 2024 14:59:14
%S 0,1,4,6,9,20,57,64,88,196,265,421,620,654,729,1587,4863,6628,12358,
%T 23773,68798,119931
%N Numbers k such that (68*10^k - 11)/3 is prime.
%C For k > 0, numbers k such that the digits 22 followed by k-1 occurrences of the digit 6 followed by the digit 3 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 226w3</a>.
%e 1 is in this sequence because (68*10^1 - 11)/3 = 223 is prime.
%e Initial terms and associated primes:
%e a(1) = 0, 19;
%e a(2) = 1, 223;
%e a(3) = 4, 226663;
%e a(4) = 6, 22666663;
%e a(5) = 9, 22666666663; etc.
%t Select[Range[0, 100000], PrimeQ[(68*10^# - 11)/3] &] (* Corrected by _Georg Fischer_, Jul 22 2019 *)
%o (PARI) isok(k) = isprime((68*10^k - 11)/3); \\ _Altug Alkan_, Oct 08 2017
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,3
%A _Robert Price_, Oct 08 2017
%E a(22) from _Robert Price_, Jan 07 2020