Kynea number

Given $n$, compute $4^n+2^{n+1}-1$ or ${(2^n+1)}^2-2$ or

$$4^n+\sum _{i=0}^n{2}^i.$$

Any of these formulas gives the Kynea number for $n$.

The first few Kynea numbers are 7, 23, 79, 287, 1087, 4223, 16639, 66047, 263167, 1050623, 4198399, 16785407, 67125247 (listed in A093069 of Sloane’s OEIS). Every third Kynea number is divisible by 7, thus prime Kynea numbers can’t have $n=3x+2$ (except of course for $n=2$. The largest Kynea number known to be prime is ${(2^{281621}+1)}^2-2$, found by Cletus Emmanuel in November of 2005, using k-Sieve from Phil Comody and OpenPFGW.

Title	Kynea number
Canonical name	KyneaNumber
Date of creation	2013-03-22 16:13:13
Last modified on	2013-03-22 16:13:13
Owner	Mravinci (12996)
Last modified by	Mravinci (12996)
Numerical id	4
Author	Mravinci (12996)
Entry type	Definition
Classification	msc 11N05