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A269797 Numbers k such that (29*10^k + 91)/3 is prime. 0

%I

%S 1,2,3,4,8,11,18,27,39,54,55,65,75,83,111,164,189,191,204,252,322,371,

%T 449,646,678,754,1641,5210,7787,11691,13682,15994,22356,29203,35756,

%U 57834,64027,72985,74276,104071

%N Numbers k such that (29*10^k + 91)/3 is prime.

%C For k>1, numbers k such that digit 9 followed by k-2 occurrences of digit 6 followed by the digits 97 is prime (see Example section).

%C a(41) > 2*10^5.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/primedifficulty.txt">Search for 96w97.</a>

%e 6 is in this sequence because (266*10^n+1)/3 = 88666667 is prime.

%e Initial terms and primes associated:

%e a(1) = 1, 127

%e a(2) = 2, 997

%e a(3) = 3, 9697

%e a(4) = 4, 96697

%e a(5) = 8, 966666697

%e a(6) = 11, 966666666697

%e a(7) = 18, 9666666666666666697

%e a(8) = 27, 9666666666666666666666666697

%e a(9) = 39, 9666666666666666666666666666666666666697 etc.

%t Select[Range[0, 100000], PrimeQ[(29*10^# + 91)/3] &]

%o (PARI) isok(n) = isprime((29*10^n + 91)/3); \\ _Michel Marcus_, Mar 05 2016

%Y Cf. A056654, A268448, A269303.

%K nonn,more

%O 1,2

%A _Robert Price_, Mar 05 2016

%E a(40) from _Robert Price_, Apr 12 2020

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Last modified August 15 13:27 EDT 2020. Contains 336504 sequences. (Running on oeis4.)