A054770
Christian G.Bower
bowerc at usa.net
Thu Jun 8 19:21:46 CEST 2000
John Conway <conway at math.Princeton.EDU> wrote:
> On Wed, 7 Jun 2000, Jud McCranie wrote:
>
> > I understand what is meant by the zeroth term, but A54770 clearly states
> > that it is using 1,3,4 (A204), not 2,1,3,4 (A32):
>
> In the original Handbook of Integer Sequences, EVERY sequence
> began with 1, whether it was logically there or not; and in the
> introduction to that book there was an explicit disclaimer making
> it clear that no official starts were being chosen.
>
> In the Encyclopedia there's a slightly different disclaimer to
> the same effect, except that there there's an entry that tells you
> which number term is the first printed one (when there's an agreed
> numbering). The fact that for the Lucas numbers this happens to be
> term number one doesn't make that into any kind of official start -
> for many sequences the first printed term is that for n = 0, and
> a few even begin with the n = 2 term (when there's some disagreement
> about the value at n = 1).
In fact, the Fibonacci numbers A000045 are listed as 1,1,2,3,5,8,...
beginning at term 0 in the book and as 0,1,1,2,3,5,8,... beginning
at term 0 in the electronic database.
Some sequences begin at term 2 or higher because the previous terms are
all 0 (as in column k of a triangle). Some begin at term 2 because
the value at term 1 is infinity. In rare cases, the sequence begins at
term -1.
> It's a more or less random editorial
> decision, probably influenced by the convention of the original
> Handbook.
>
> John Conway
Christian
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