[seqfan] Re: A comment in A001045

Andrew Weimholt andrew.weimholt at gmail.com
Sat Dec 5 01:59:56 CET 2009

It looks like he is trying to say k -> 2^n-k, where the k on the right
is the current a(n) and the k on the left is a(n+1).

A better way to state this is
a(n+1) = 2^n - a(n)    for n>0, a(0)=0
(which I am surprised to find missing from the formula section, or
maybe I just didn't look hard enough).

This is equivalent to the comment by Amarnath Murthy...
Sums of pair of consecutive terms give all powers of 2 in increasing
order. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Aug 15 2002

Andrew

On 12/4/09, Klaus Brockhaus <klaus-brockhaus at t-online.de> wrote:
> %N A001045 Jacobsthal sequence (or Jacobsthal numbers): a(n) = a(n-1) +
>  2a(n-2), with a(0) = 0, a(1) = 1.
>
>  has a comment
>
>  %C A001045 General form: k=2^n-k. [From .........., Dec 11 2008]
>
>  Can someone (the author?) please explain what this means?
>
>  Klaus Brockhaus
>
>
>
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