[seqfan] Re: A true Mac Mahon ruler?
wild at music.mcgill.ca
Tue Jun 25 23:21:37 CEST 2019
Hi Eric - is it possible you are thinking of a Golomb ruler instead? A
Golomb ruler has the requirement you are interested in, that no distance
can be measured in two different ways. Golomb rulers that measure every
distance up to n are called *perfect*, and the longest known perfect
Golomb ruler has length 6. So you will definitely not find one to measure
up to 200!
A003022 has the list of optimal Golomb rulers.
On Tue, 25 Jun 2019, Éric Angelini wrote:
> Hello SeqFans,
> The first 8 terms of A002049 are:
> 1,3,7,12,20,30,44 and 59.
> I see that I can measure 29 in two
> ways with this ruler (I thought only
> one way was authorized):
> I am obviously missing smthg as this
> is an ancient seq. signed by Neil himself.
> Anyway -- is it possible to build a
> wooden ruler with as few as possible
> vertical marks such that all integers
> measures between 1 and 200 can
> be materialized only once?
> I guess this sort of question is as
> old as the hat I'm wearing right now to
> avoid the killer sun we currently have
> in Brussels. Forgive me.
> (and if this seq is already
> in the OEIS, my shame will
> be complete).
> Seqfan Mailing list - http://list.seqfan.eu/
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