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Numbers k such that (28*10^k - 43)/3 is prime.
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%I #18 Jun 06 2024 23:24:04

%S 1,2,3,4,5,6,7,13,43,112,114,127,242,247,251,335,450,616,816,1237,

%T 1448,4303,4865,5414,6427,9045,10391,12651,25071,27901,50362,58843,

%U 67378,68107,262655

%N Numbers k such that (28*10^k - 43)/3 is prime.

%C For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 3 followed by the digits 19 is prime (see Example section).

%C a(36) > 3*10^5.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 93w19</a>.

%e 3 is in this sequence because (28*10^3 - 43)/3 = 9319 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 79;

%e a(2) = 2, 919;

%e a(3) = 3, 9319;

%e a(4) = 4, 93319;

%e a(5) = 5, 933319, etc.

%t Select[Range[0, 100000], PrimeQ[(28*10^# - 43)/3] &]

%o (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime((28*10^n - 43)/3), print1(n, ", "))); \\ _Altug Alkan_, Apr 05 2016

%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

%K nonn,more

%O 1,2

%A _Robert Price_, Apr 05 2016

%E a(35) from _Robert Price_, Jul 02 2023