[seqfan] Re: Romans with toothpicks

franktaw at netscape.net franktaw at netscape.net
Tue Jan 5 17:57:42 CET 2010


Just after I submitted my mail, I found 
http://www.research.att.com/~njas/sequences/A002963, which at least 
provides an answer to my questions up to 4000.  (And "chisel strokes" 
is a better description than "toothpicks".)  So if we say one chisel 
stroke to multiply by 1000 from 'V' on, we have a reasonably simple and 
standard definition.  So I guess I withdraw my objection.

I still wouldn't submit the sequence, myself.

Franklin T. Adams-Watters

-----Original Message-----
From: Eric Angelini <Eric.Angelini at kntv.be>

You're right, Franklin... As always, just
after submitting I "saw" the C -- then the D...
We could exclude integers written with those
letters, but... mhâââ, this becomes too com-
plicated -- thus ugly!
Best,
É.


-----Message d'origine-----
De : seqfan-bounces at list.seqfan.eu 
[mailto:seqfan-bounces at list.seqfan.eu] De la
part de franktaw at netscape.net
Envoyé : mardi 5 janvier 2010 16:41
À : seqfan at list.seqfan.eu
Objet : [seqfan] Re: Romans with toothpicks

Well, now, that does raise some questions.  Is 'X' written with 2
toothpicks or 4?  (Apparently 2 from your data, but it isn't obvious a
priori.)  Are 'C' and 'D' available?  If so, how many toothpicks do
they use?  I could see 2 and 3, respectively, or 0 and 1 (with the
curved parts represented some other way); or maybe you bend the
toothpicks and get 1 and 2.  'M' presumable uses 4.  5000 may be
expressed with 5 M's, or with an underlined or overlined 'V'; in the
latter case, it would presumably require 3 toothpicks.  Then for 15000,
do we use a single toothpick to underline both the 'X' and the 'V', or
are they separate?

Franklin T. Adams-Watters

P.S. Just my opinion, but -- ick.  Bad enough that it's another Roman
numeral sequence, but posing problems of how to define it on top of
that ....

-----Original Message-----
From: Eric Angelini <Eric.Angelini at kntv.be>

S = 1,2,3,6,9,10,12,20,30...

Integers which, when written in Roman numbers with toothpicks,
are divisible by the quantity of toothpicks they use.

Best,
É.


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