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Numbers k such that (16*10^k - 19)/3 is prime.
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%I #17 Jun 06 2024 23:24:20

%S 1,4,5,6,10,13,20,22,24,35,41,42,46,155,222,336,432,538,577,637,679,

%T 750,758,785,2262,5436,6806,7962,9757,16016,24588,47918,59062,74092,

%U 81896,85495,102299,185978,190420

%N Numbers k such that (16*10^k - 19)/3 is prime.

%C For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 3 followed by the digits 27 is prime (see Example section).

%C a(40) > 2*10^5.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 53w27</a>.

%e 4 is in this sequence because (16*10^4 - 19)/3 = 53327 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 47;

%e a(2) = 4, 53327;

%e a(3) = 5, 533327;

%e a(4) = 6, 5333327;

%e a(5) = 10, 53333333327;

%e a(6) = 13, 53333333333327, etc.

%t Select[Range[0, 100000], PrimeQ[(16*10^# - 19)/3] &]

%o (PARI) lista(nn) = {for(n=1, nn, if(ispseudoprime((16*10^n - 19)/3), print1(n, ", ")));} \\ _Altug Alkan_, Mar 31 2016

%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A270974.

%K nonn,more

%O 1,2

%A _Robert Price_, Mar 31 2016

%E a(37)-a(39) from _Robert Price_, Feb 23 2019