[seqfan] Re: A true Mac Mahon ruler?

[Éric Angelini]

Hi Jon,
thanks for yr answer -- yes, this is
exactly what I was looking for -- and
I notice now that the whole subject
has been thoroughly analyzed and 
put into the OEIS!
I'm reading more on the subject and
will try to deeply understand the
rules of the perfect rulers!
Many thanks again!
à+
É.
Catapulté de mon aPhone


> Le 25 juin 2019 à 23:21, Jon Wild <wild at music.mcgill.ca> a écrit :
> 
> 
> 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.
> 
> Jon
> 
> 
>> 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):
>> 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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> 
> 
> 
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