[seqfan] Re: A true Mac Mahon ruler?

[Kerry Mitchell]

A002049 references A002048, which contains a link to an article:

https://www.jstor.org/stable/2318498?seq=1#metadata_info_tab_contents

>From there you can see that there's no requirement that each integer can
only be measured once. Quoting, "MacMahon posed the problem of placing
division marks on an infinite rule so that every integral distance can be
measured between some two division points on the ruler..."

Kerry


On Tue, Jun 25, 2019 at 11:00 AM Éric Angelini <eric.angelini at skynet.be>
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):
> 30-1=29
> 59-30=29
> 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).
> Best,
> É.
>
>
>
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