[seqfan] Re: computability of A080075 Proth numbers

[Georgi Guninski]

On Mon, Aug 16, 2010 at 04:12:19PM +0200, Maximilian Hasler wrote:
> I considered the sequence
> b = min( -a[i-1]+2*a[i],  -2*a[i-1]+3*a[i] )
> 
> which turns out to be
>  b[i] = a[i] + 2^m[i]
> with
> m[2] = 1,
> m[3..5] = 2, [3 terms]
> m[6..11] = 3 [6 terms],
> m[12..23] = 4 [12 terms],
> m[24..47] = 5 [24 terms], etc...
>

lol, if i have computed your b(n) correctly:

5, 7, 13, 17, 21, 33, 41, 49, 57, 65, 73, 97, 113, 129, 145, 161, 177, 193, 209, 225

to 10 000:

b(n+1) =  -7/2*b(n - 2) + 4*b(n - 1)+ 1/2*b(n)
OR ;-)
b(n+1) = -b(n - 1) + 2*b(n) 

(the second branch is more probable except for: 10,11,22,23,46,47,94,95 ...)