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

Hans Havermann pxp at rogers.com
Wed Mar 31 06:52:59 CEST 2010

```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