[seqfan] Re: A001045 General form: k=2^n-k

franktaw at netscape.net franktaw at netscape.net
Sat Dec 5 10:09:05 CET 2009

```Vladimir,

The problem is not with the phrase "general form", but with "k=2^n-k".
As you are using it, this is a programming language construct
(specifically Mathematica).  You need to put it into mathematical
language instead.  When "k=2^n-k" is interpreted mathematically, it is
a statement of equality; it can be manipulated algebraically to "2k =
2^n", and hence k = 2^(n-1).

The correct form would be something like "a(n) = 2^n - a(n-1)".

-----Original Message-----

*Message: 7
Date: Sat, 05 Dec 2009 01:14:21 +0100
From: Klaus Brockhaus
<**klaus-brockhaus at t-online.de*<klaus-brockhaus at t-online.de>
*>
Subject: [seqfan]  A comment in A001045*
*%C A001045 General form: k=2^n-k.*
*Can someone (the author?) please explain what this means?
*
*
*
1. as you can see : *k=2^n-k *is the same for many seqs.

k=-2;lst={k};Do[k=2^n-k;AppendTo[lst,k],{n,0,4!}];lst(*A083594.*)
k=-1;lst={k};Do[k=2^n-k;AppendTo[lst,k],{n,0,4!}];lst(*A084247,
A097073.*)
k=0;lst={k};Do[k=2^n-k;AppendTo[lst,k],{n,0,4!}];lst(*A001045
Jacobsthal
sequence.*)
k=1;lst={k};Do[k=2^n-k;AppendTo[lst,k],{n,0,4!}];lst(*A014113,
A078008.*)
k=2;lst={k};Do[k=2^n-k;AppendTo[lst,k],{n,0,4!}];lst(*A140966.*)
k=3;lst={k};Do[k=2^n-k;AppendTo[lst,k],{n,0,4!}];lst(*A154879.*)
k=4;lst={k};Do[k=2^n-k;AppendTo[lst,k],{n,0,4!}];lst(*A115335.*)

2. if frase `*General form*` is Not appropriate for this explanation..
I do Not hold on this.
This is merely a sample/example/observation...
I'm Not insists on name/frase/form ...etc.

p.s.
we have many seqs, wich can be written by one `general` formula(s),
maybe we need some kind of classification, as / or similar as in
Biology?
then one derivatives from other...
some kind of order and sence,
and Not ... ten thousands of segs, but Not related to each other...
millions-green-man-born-independently-in-the-different-galaxies-and-have-
absolutly-nothing-to-say-to-each-other.
--