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

4, 6, 8, 11, 12, 14, 23, 26, 42, 50, 54, 55, 66, 136, 145, 151, 200, 214, 888, 896, 1674, 2311, 2799, 2836, 2912, 5192, 5907, 8644, 8681, 11914, 18140, 27383, 36549, 57358, 84582, 161253, 167639, 186842, 193230, 204764

Offset: 1

Author

Robert Price, Mar 17 2016

Keywords

• nonn
• more

Comments

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

a(41) > 3*10^5.

Examples

			4 is in this sequence because 10^4-8001 = 1999 is prime.
Initial terms and associated primes:
a(1) = 4, 1999;
a(2) = 6, 991999;
a(3) = 8, 99991999;
a(4) = 11, 99999991999;
a(5) = 12, 999999991999, etc.
		

Links

• Makoto Kamada, Search for 9w1999.

Crossrefs

Cf. A056654, A268448, A269303, A270339.

Programs

Maple

isa := n -> isprime(10^n-8001):
select(isa, [$0..1000]); # Peter Luschny, Jul 22 2019

Mathematica

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

PARI

isok(n) = isprime(10^n-8001); \\ Michel Marcus, Mar 18 2016

PARI

lista(nn) = for(n=1, nn, if(ispseudoprime(10^n-8001), print1(n, ", "))); \\ Altug Alkan, Mar 18 2016

Extensions

a(36)-a(39) from Robert Price, Mar 27 2018

a(40) from Robert Price, May 31 2023