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%I #16 May 26 2024 14:58:10
%S 0,2,5,6,11,14,41,47,51,84,164,228,293,1178,1212,1292,2099,2694,4446,
%T 7382,13638,39428,40971
%N Numbers k such that (728*10^k - 71)/9 is prime.
%C For k > 0, numbers k such that the digits 80 followed by k-1 occurrences of the digit 8 followed by the digit 1 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 808w1</a>.
%e 2 is in this sequence because (728*10^2 - 71)/9 = 8081 is prime.
%e Initial terms and associated primes:
%e a(1) = 0, 73;
%e a(2) = 2, 8081;
%e a(3) = 5, 8088881;
%e a(4) = 6, 80888881;
%e a(5) = 11, 8088888888881; etc.
%t Select[Range[0, 100000], PrimeQ[(728*10^# - 71)/9] &]
%o (PARI) isok(k) = isprime((728*10^k - 71)/9); \\ _Altug Alkan_, Oct 08 2017
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Oct 08 2017