Re: number sequence

Am 31.08.05 04:44 schrieb quasi:

> On 30 Aug 2005 16:32:04 -0700, "Russ" <rwpatterson@xxxxxxx> wrote:
>
>
>>Hi:
>>
>>How should I go about trying to determine the equation that results in
>>a number sequence like this:
>>
>>2, 6, 22, 86, 342...
>>
>>I see the difference between each term is a power of 2 but am stuck on
>>how to determine equation. e.g. difference between 86 and 342 is 2^8.
>>
>>thanks,
>>russ
>
>
> Look at the terms as sums:
>
> 2=1+1
> 6=1+1+4
> 22=1+1+4+4^2
> 86=1+1+4+4^2+4^3
> 342=1+1+4+4^2+4^3+4^4
>
I like to display such solutions in number-base-systems
with digits; select base-4 here:
(base 10) (base 4)
2 = 1 + 1
6 = 1 + 11
22 = 1 + 111
86 = 1 + 1111
342 = 1 + 11111
...

and the repunit is for any base, as Arturo Magidin already pointed out,

a^n - 1
-------- = 1111111...1 (n times 1)
a - 1

so the next should be

(base 4) (base 10)
333333 4^6-1
x= 1+ -------- = 1 + -------
3 3

Gottfried Helms
.

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