A098855 Numbers k such that 4^k + 2^k - 1 is prime.

1, 2, 3, 4, 6, 10, 16, 24, 26, 35, 52, 55, 95, 144, 379, 484, 939, 1284, 1300, 2651, 3644, 3979, 7179, 8304, 14840, 32040, 38906, 47759, 51371, 52484, 54016, 57279

Offset: 1

Author

Pierre CAMI, Oct 11 2004

Keywords

• nonn
• more
• hard

Comments

Or, numbers k such that (2^k+1)*2^k - 1 is prime.

Examples

			1300 is in the sequence because 4^1300+2^1300-1 is prime.
4^1+2^1-1 = 5 prime so a(1)=1.
4^2+2^2-1 = 19 prime so a(2)=2.
4^3+2^3-1 = 71 prime so a(3)=3.
4^4+2^4-1 = 271 prime so a(4)=4.
		

Links

• F. Firoozbakht and M. F. Hasler, Variations on Euclid's formula for Perfect Numbers, JIS 13 (2010) #10.3.1

Crossrefs

Cf. A110079, A110082, A210733.

Programs

Mathematica

Do[If[PrimeQ[4^m+2^m-1], Print[m]], {m, 8000}] (* Farideh Firoozbakht, Aug 03 2005 *)

PARI

is(n)=ispseudoprime(4^n+2^n-1) \\ Charles R Greathouse IV, Jun 13 2017

Formula

A110082(n) = 2^(a(n)-1)*(4^a(n)+2^a(n)-1).

Extensions

Corrected by Torin Huzil (thuzil(AT)gmail.com), Sep 15 2005

More terms from Pierre CAMI, May 10 2012

a(27), a(29)-a(31) inserted by Michael S. Branicky, Jan 02 2025