A054770

[John Conway]

On Wed, 7 Jun 2000 karttu at megabaud.fi quoted and wrote:

> >  > I think that basically you have forgotten the zeroth Lucas number 2,
> > >present in the alternative entry of the Lucas sequence in EIS:
> > >
> > >ID Number: A000032 (Formerly M0155)
> > >Sequence:  2,1,3,4,7,11,18,29,47,76,123,199,322,521,843,1364,2207,3571,
> > 
> > That is a different (generalized) Lucas sequence.  You can pick the first 
> > two terms for a Fibonacci or Lucas sequence.  The standard Fibonacci starts 
> > with 1,2 and the standard Lucas numbers start with 1,3.

    I think that's an unhelpful remark. There's no universally
agreed "start" to either sequence.  What IS universally agreed is
the numbering of the two sequences:

    n   0  1  2  3  4  5  6  7  8 ...
   Fn   0  1  1  2  3  5  8 13 21 ...
   Ln   2  1  3  4  7 11 18 29 47 ...

so that all you mean is that you prefer to start the Fibonacci
sequence at the terms  F2, F3  and the Lucas one at  L1, L2.

    I'm sure many people would prefer to start the Fibonacci one
with  F1,F2,  while others prefer to include the n=0 terms.  I'm
sure most mathematicians (myself included) don't think it sensible
to choose any fixed start.

    John Conway