Early Bird numbers

Mon Jul 23 05:41:32 CEST 2007

sent a really nice sequence:
 introduced by Martin Gardner in the November 2005 issue of Math. Horizons, published by the
 member.
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Date: Mon, 23 Jul 2007 14:39:19 +0700
From: "Warut Roonguthai" <warut822 at gmail.com>
To: seqfan at ext.jussieu.fr
Subject: Re: Early Bird numbers
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Here are the first 157 terms of the early bird sequence:

12,21,23,31,32,34,41,42,43,45,51,52,53,54,56,61,62,63,64,65,
67,71,72,73,74,75,76,78,81,82,83,84,85,86,87,89,91,92,93,94,
95,96,97,98,99,101,110,111,112,121,122,123,131,132,141,142,
151,152,161,162,171,172,181,182,191,192,201,202,210,211,
212,213,214,215,216,217,218,219,220,221,222,223,231,232,
233,234,241,242,243,251,252,253,261,262,263,271,272,273,
281,282,283,291,292,293,301,302,303,310,311,312,313,314,
315,316,317,318,319,320,321,322,323,324,325,326,327,328,
329,330,331,332,333,334,341,342,343,344,345,351,352,353,
354,361,362,363,364,371,372,373,374,381,382,383,384,391,
392,393,394

Note that the natural place of n begins at

dn + 1 - (10^d - 1)/9

where d is the number of decimal digits of n, i.e.,

d = floor(log10(n)) + 1

Can this be a new sequence too?

BTW, I don't have access to Martin Gardner's article.

Warut

On 7/23/07, N. J. A. Sloane <njas at research.att.com> wrote:
>
> Dear Seqfans,  My old friend Bernardo Recaman Santos just
> sent a really nice sequence:
>
> %I A116700
> %S A116700 12,21,23,31,32,34,41,42,43
> %N A116700 "Early bird" numbers: write the natural numbers in a string 12345678910111213....
> Sequence gives numbers which occur in the string ahead of their natural place.
> %C A116700 Based on an idea by Argentinian puzzle creator Jaime Poniachik, these numbers were
>  introduced by Martin Gardner in the November 2005 issue of Math. Horizons, published by the
> MAA.
> %e A116700 "12" appears at the start of the string, ahead of its position after "11", so is a
>  member.
> %K A116700 nonn,base,more,nice,new
> %O A116700 1,1
> %A A116700 Bernardo Recaman Santos (ignotus(AT)hotmail.com), Jul 22 2007
>
> One needs to be a subscriber to have on-line access to
> Math Horizons - can anyone get me a copy of the Martin Gardner
> article?
>
> Neil
>