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A270448 Numbers k such that 10^k - 8001 is prime.

%I A270448 #28 May 02 2024 22:54:36
%S A270448 4,6,8,11,12,14,23,26,42,50,54,55,66,136,145,151,200,214,888,896,1674,
%T A270448 2311,2799,2836,2912,5192,5907,8644,8681,11914,18140,27383,36549,
%U A270448 57358,84582,161253,167639,186842,193230,204764
%N A270448 Numbers k such that 10^k - 8001 is prime.
%C A270448 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 A270448 a(41) > 3*10^5.
%H A270448 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 9w1999</a>.
%e A270448 4 is in this sequence because 10^4-8001 = 1999 is prime.
%e A270448 Initial terms and associated primes:
%e A270448 a(1) = 4, 1999;
%e A270448 a(2) = 6, 991999;
%e A270448 a(3) = 8, 99991999;
%e A270448 a(4) = 11, 99999991999;
%e A270448 a(5) = 12, 999999991999, etc.
%p A270448 isa := n -> isprime(10^n-8001):
%p A270448 select(isa, [$0..1000]); # _Peter Luschny_, Jul 22 2019
%t A270448 Select[Range[0, 100000], PrimeQ[10^#-8001 && # > 3] &] (* Corrected by _Georg Fischer_, Jul 22 2019 *)
%o A270448 (PARI) isok(n) = isprime(10^n-8001); \\ _Michel Marcus_, Mar 18 2016
%o A270448 (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime(10^n-8001), print1(n, ", "))); \\ _Altug Alkan_, Mar 18 2016
%Y A270448 Cf. A056654, A268448, A269303, A270339.
%K A270448 nonn,more
%O A270448 1,1
%A A270448 _Robert Price_, Mar 17 2016
%E A270448 a(36)-a(39) from _Robert Price_, Mar 27 2018
%E A270448 a(40) from _Robert Price_, May 31 2023