[seqfan] Re: computability of A080075 Proth numbers

[Georgi Guninski]

On Mon, Aug 16, 2010 at 04:12:19PM +0200, Maximilian Hasler wrote:
> > a(n+1) = (-a(n - 1) + 2*a(n))
> > OR
> > a(n+1) = (-2*a(n - 1) + 3*a(n))
> 

looks like the first branch of the OR is TRUE unless n=2^k (else the
second branch is correct).

assuming the formulas are correct this bugs me:
unless n=2^k proth numbers satisfy a linear recurrences, yet the
doubling formulas are linear.


> I considered the sequence
> b = min( -a[i-1]+2*a[i],  -2*a[i-1]+3*a[i] )
>

this usage of |min| reminds me of "tropical semiring" where
x "+" y <-> min(x,y)
x "*" y <-> x + y

couldn't find any interesting "tropical" stuff, though...

-- 
joro