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%I #24 May 26 2024 15:49:09
%S 0,1,2,3,4,5,6,8,10,13,19,26,37,69,77,81,214,242,255,900,1113,1833,
%T 3166,3566,4753,4849,4869,5005,7372,7702,10240,16100,18972,28574,
%U 33815,37820,70457,89482,106066,133603,154897,278325
%N Numbers k such that (266*10^k + 1)/3 is prime.
%C For k > 0, numbers k such that digits 88 followed by k-1 occurrences of digit 6 followed by the digit 7 is prime (see Example section).
%C a(43) > 3*10^5.
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 886w7</a>.
%e 6 is in this sequence because (266*10^n+1)/3 = 88666667 is prime.
%e Initial terms and associated primes:
%e a(1) = 0, 89;
%e a(2) = 1, 887;
%e a(3) = 2, 8867;
%e a(4) = 3, 88667;
%e a(5) = 4, 886667;
%e a(6) = 5, 8866667;
%e a(7) = 6, 88666667;
%e a(8) = 8, 8866666667;
%e a(9) = 10, 886666666667;
%e a(10) = 13, 886666666666667, etc.
%t Select[Range[0, 100000], PrimeQ[(266*10^#+1)/3] &]
%o (Magma) [n: n in [0..220] | IsPrime((266*10^n + 1) div 3)]; // _Vincenzo Librandi_, Feb 23 2016
%o (PARI) is(n)=ispseudoprime((266*10^n + 1)/3) \\ _Charles R Greathouse IV_, Feb 16 2017
%Y Cf. A056654, A268448.
%K nonn,more
%O 1,3
%A _Robert Price_, Feb 22 2016
%E a(39)-a(41) from _Robert Price_, Apr 22 2020
%E a(42) from _Robert Price_, May 31 2023