# Prime numbers of the form : $2^{n+a}+2^{n} \pm 1$ , where $0 \leq a < n$ and $n \equiv 0 \pmod 6$

Is it true that :

For any positive integer $n$ such that $n \equiv 0 \pmod 6$ there is at least one prime number of the form:

$p=2^{n+a}+2^{n} + 1$ , or , $p=2^{n+a}+2^{n} - 1$

with following properties : $0 \leq a < n$ , and $a\in \mathbf{Z^{*}} ; n\in \mathbf{Z^{+}}$

I have checked statement for each $n$ up to $n=1002$ and I haven't found any counterexample.

Any idea how to prove or disprove statement above without using a computer?

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IOW, OTF $64^m(2^a+1)\pm1,m\in\mathbb{N},0\le a<6m$. –  anon Nov 7 '11 at 12:16
related sequence –  pedja Nov 8 '11 at 6:57