Integer "observables"

[Andrew Plewe]

something I've been thinking about for awhile. Imagine that you had an
so, is there any way to count the increase? I don't know if any of this can
	-Andrew Plewe-
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Subject: earliest string to reprsent 00 ... 99
Cc: njas at research.att.com
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Date: Wed, 13 Feb 2008 20:50:07 -0800
From: "Joshua Zucker" <joshua.zucker at gmail.com>
To: "Sequence Fans" <seqfan at ext.jussieu.fr>
Subject: Re: earliest string to reprsent 00 ... 99
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I don't think the given seq. contains 90 or 9,0 in it, so either
there's a mistake or we're misunderstanding the sequence.
--Joshua Zucker


On Feb 13, 2008 7:44 PM, N. J. A. Sloane <njas at research.att.com> wrote:
>
> Dear Seqfans, Patrick A. Kirol submitted a sequence
> which I did not understand.  After reading his reply,
> I think that the problem can be stated as follows:
>
> Find the shortest (and lexicographically earliest)
> decimal string which contains all the 2-digit strings 01, 02,
> ..., 98, 99.
>
> Presumably something like this will be optimal:
>
> 1 0 1 1 2 1 3 ... 9 9
>
> Here is what he sent me:
>
> %S A000001 0,01,02,03,04,05,06,07,08,09,1,12,13,14,15,16,17,18,19,2,23,24,25,26,27,28,29,3,34,35,36,37,38,39,4,45,46,47,48,49,5,56,57,58,59,6,67,68,69,7,78,79,8,89,9
>
> but I think the version in the
> OEIS should be a string of single digits seperated by commas.
> The string /could/ begin with 0, but it's not obvious that that
> is optimal.
>
> Neil
>
>
>