# [seqfan] Re: Wajnberg variations (100 terms and percentages)

Allan Wechsler acwacw at gmail.com
Thu Oct 2 18:37:25 CEST 2014

```Then I do not understand why you exclude, for example,

{1,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99}

On Thu, Oct 2, 2014 at 12:15 PM, Eric Angelini <Eric.Angelini at kntv.be>
wrote:

> (message has left my computer before I could end it, sorry)
>
> Hello Allan,
> my idea (badly exposed, I'm afraid) is that we must have
> 100 elements in the set -- and every single element "speaks"
> and "says":
> « There are fourteen '14's in this set » (if '14' speaks)
> or:
> « There is one '1' in this set » (if '1' speaks)
> etc.
> Best,
> É.
>
>
>
> -----Message d'origine-----
> De : SeqFan [mailto:seqfan-bounces at list.seqfan.eu] De la part de Allan
> Wechsler Envoyé : jeudi 2 octobre 2014 17:27 À : Sequence Fanatics
> Discussion list Objet : [seqfan] Re: Wajnberg variations (100 terms and
> percentages)
>
> I think I am not really understanding the rules.
>
> Let us abbreviate a sequence of n n's, then m m's, and so on, as [n,m...];
> for example, "2,2,3,3,3" would be written "[2,3]".
>
> Then Eric's S% is [1,2,3,4,6,7,8,9,10,11,12,13,14]; T% =
> [1,4,5,6,7,8,9,10,11,12,13,14]; U% = [2,3,5,6,7,8,9,10,11,12,13,14]. Then
> he says that these are the only such 100-sequences. What is wrong with,
> say, [1,99]? Or [4,5,6,12,30,43]? What additional constraint is there
> besides that it must be a partition of 100 into blocks of distinct sizes?
>
> On Thu, Oct 2, 2014 at 6:16 AM, Eric Angelini <Eric.Angelini at kntv.be>
> wrote:
>
> > Hello SeqFans,
> > here are 3 seq I've discussed with my friend Alexandre W.
> > S%, T% and U% are 3 finite seq of 100 terms each.
> > They self-describe their content in a "percentage way":
> >
> > S% =
> >
> 1,2,2,3,3,3,4,4,4,4,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,14,14,14,14,14,14.
> >
> > T% =
> >
> >
> 1,4,4,4,4,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,14,14,14,14,14,14.
> >
> > U% =
> >
> >
> 2,2,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,14,14,14,14,14,14.
> >
> > Explanation (for U%, immediately above):
> >
> > Among the 100 terms of U%, only two are '2' --> there is 2% of '2'
> > Among the 100 terms of U%, only three are '3' --> there is 3% of '3'
> > Among the 100 terms of U%, only five are '5' --> there is 5% of '5'
> > Among the 100 terms of U%, only six are '6' --> there is 6% of '6'
> > ...
> > Among the 100 terms of U%, only fourteen are '14' --> there is 14% of
> '14'
> > END.
> >
> > Those are the only such 100-term possible seq -- and S% is the
> > lexically first (then T%, then U%).
> > A 1000-term such seq is easy to build. And a 10,000 one also, etc.
> > But is it possible to build an infinite seq like that? Well, there is
> > at least this one : H% = 100,100,100,100,100,100,100,100,...
> > ;-D
> > Best,
> > É.
> >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
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