A296443 Numbers k such that 2*10^(2k)-2*10^k+1 is prime.

1, 2, 6, 7, 8, 315, 667, 5125, 7301, 10500, 11096

Offset: 1

Author

Patrick A. Thomas, Dec 13 2017

Keywords

• nonn
• more

Comments

Numbers of this form divide 4*10^(4k)+1.

a(8) > 5000. - Jon E. Schoenfield, Dec 16 2017

a(12) > 25000. - Michael S. Branicky, Aug 08 2024

Examples

			181, 19801, 1999998000001, 199999980000001, and 19999999800000001 are prime, while 1998001=277*7213, 199980001=13*41*457*821, and 19999800001=53*5953*63389.
		

Crossrefs

See A296444 for 2*10^(2k)+2*10^k+1.

Programs

Mathematica

ParallelMap[If[PrimeQ[2*10^(2 #) - 2*10^# + 1], #, Nothing] &, Range@ 4000] (* Robert G. Wilson v, Dec 13 2017 *)

PARI

isok(k) = isprime(2*10^(2*k)-2*10^k+1); \\ Michel Marcus, Dec 13 2017

Extensions

a(6)-a(7) from Michel Marcus, Dec 13 2017

a(8)-a(11) from Michael S. Branicky, Mar 31 2023