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Numbers k such that 10^k - 8001 is prime.
0

%I #28 May 02 2024 22:54:36

%S 4,6,8,11,12,14,23,26,42,50,54,55,66,136,145,151,200,214,888,896,1674,

%T 2311,2799,2836,2912,5192,5907,8644,8681,11914,18140,27383,36549,

%U 57358,84582,161253,167639,186842,193230,204764

%N Numbers k such that 10^k - 8001 is prime.

%C For k > 3, numbers k such that k-4 occurrences of the digit 9 followed by the digits 1999 is prime (see Example section).

%C a(41) > 3*10^5.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 9w1999</a>.

%e 4 is in this sequence because 10^4-8001 = 1999 is prime.

%e Initial terms and associated primes:

%e a(1) = 4, 1999;

%e a(2) = 6, 991999;

%e a(3) = 8, 99991999;

%e a(4) = 11, 99999991999;

%e a(5) = 12, 999999991999, etc.

%p isa := n -> isprime(10^n-8001):

%p select(isa, [$0..1000]); # _Peter Luschny_, Jul 22 2019

%t Select[Range[0, 100000], PrimeQ[10^#-8001 && # > 3] &] (* Corrected by _Georg Fischer_, Jul 22 2019 *)

%o (PARI) isok(n) = isprime(10^n-8001); \\ _Michel Marcus_, Mar 18 2016

%o (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime(10^n-8001), print1(n, ", "))); \\ _Altug Alkan_, Mar 18 2016

%Y Cf. A056654, A268448, A269303, A270339.

%K nonn,more

%O 1,1

%A _Robert Price_, Mar 17 2016

%E a(36)-a(39) from _Robert Price_, Mar 27 2018

%E a(40) from _Robert Price_, May 31 2023