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From: jpl@allegra.UUCP (John P. Linderman)
Newsgroups: net.math
Subject: Re: Fib[0] is 0, not 1
Message-ID: <2738@allegra.UUCP>
Date: Mon, 27-Aug-84 09:35:20 EDT
Article-I.D.: allegra.2738
Posted: Mon Aug 27 09:35:20 1984
Date-Received: Tue, 28-Aug-84 00:13:15 EDT
References: <19@tekchips.UUCP>, <8772@watmath.UUCP>
Organization: AT&T Bell Laboratories, Murray Hill
Lines: 22

>Steve Vegdahl says:
>> In response to a recent article part of whose definition of fib was:
>> 	if n < 2 then fib := 1
>> This should have been (assuming n positive):
>> 	if n < 2 then fib := n
>> The sequence is
>> 	0, 1, 1, 2, 3, 5, 8 ...
>> not
>> 	1, 1, 2, 3, 5, 8 ...
>
>I tend to agree, but the properties of this sequence that make it
>interesting to me do not depend on how many initial terms one omits.

The question is one of indexing, not of omitting.  One of my
favorite identities involves Fibonacci numbers and greatest
common divisors, namely

    GCD(fib(i), fib(j)) = fib(GCD(i,j))

but it relies on the "proper" indexing of the Fibonacci's.

John P. Linderman  Small fib Department  allegra!jpl