[seqfan] Re: Big Numbers in the Champernowne Continued Fraction Expansion

Alonso Del Arte alonso.delarte at gmail.com
Wed Mar 31 23:46:00 CEST 2010

Well, at a general level, if we can reasonably assume that researchers
investigating a particular problem are just as likely to come up with
sequence A as they are sequence B and then look it up, then both sequences
ought to be in the OEIS. Usefulness trumps consistency.

In the particular case of the Champernowne constant, I've started looking
at Eric's notebook but have yet to come to any conclusion.


On Wed, Mar 31, 2010 at 12:52 AM, Hans Havermann <pxp at rogers.com> wrote:

> Alonso Del Arte:
> > Does A038705(0) = 1 sound correct to you?
> Why does even this simple question seem so complicated to me?
> The simple continued fraction expansion for Champernowne is 0, 8, 9,
> 1, 149083, ... (A030167, offset-zero). The positions of the
> incrementally largest terms therein are 2, 3, 5, ... (my A038705,
> offset-one). Why didn't I start with 1? It was unclear to me ten years
> ago that I needed to. Perhaps the word "incrementally" suggested to my
> mind that the initial term be ignored. More likely I used a template,
> such as Eric Weisstein's 2, 5, ... (A033263, offset-one), positions of
> the incrementally largest terms in 0, 1, 1, 1, 27, ... (A033260,
> offset-one: it should be offset-zero, I think) as a guide.
> Eric's submission of 0, 1, 2, 4, ... (A143533) differs in substance
> from his own many-years-earlier submission (above) in three distinct
> ways:
> #1. He considers and prepends that first term.
> #2. He uses index numbers instead of position numbers.
> #3. He gives it an offset-zero instead of offset-one.
> With regard to #1, is there now any consistency in the database with
> such "position" sequences? Perhaps it depends on the wording in the
> definition. Should there be consistency? Will one retrofit sequences
> to conform to an established norm?
> With regard to #2, I actually prefer index numbers. I used them in my
> http://chesswanks.com/pxp/cfcd.html
>  wherein I suggest explicitly that position = index + 1, but of
> course one's linguistic mileage will vary. At any rate, I submitted
> A038705 as position numbers instead of index numbers back then
> because, at the time, that's how I saw it being done. The previous
> question about retrofitting applies.
> With regard to #3, I'm not at all sure but I think it's offset-one
> irrespective of what one does in either #1 or #2.
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