Re: just 5 quick answers then I can summarise and GO

From: ken quirici (kquirici_at_yahoo.com)
Date: 01/10/05 

Date: 10 Jan 2005 12:03:00 -0800

george wrote:
The subject line is laughable.
> The only quick answer to a stupid (and stupidly formed)
> question is "that's a stupid question". All substantive

There might be it seems to me an interesting or semi-interesting
question in that first post, assuming the strings of digits in the
(B)string are, or become after some finite time, sequences of
repeating groups of digits. For example, in the following string
of digits, where the '/' shows where the repeating group repeats,
one of the (B) strings could be

......1254980894/1254980894/......

The question is, maybe, what is the longest string of digits in pi (or
any irrational) that is a group of digits repeated 'n' times?

There might be a number-theoretic issue here - how 'rational' can an
irrational sequence of digits get? There doesn't seem to be any other
issue since it seems clear that there can't be an INFINITE repeating
string in the decimal representation of pi. If there were, it would
take up all but a finite part of pi, and so pi would be rational. This
is true I think but the proof eludes me.

Maybe this: let n be the digit at which a group starts that repeats an
infinite number of times. Let p be the digit at which the group stops
repeating. But since the group repeats an infinite number of times,
p will occur in the middle of the repetitions. That ok?

Thanks.

Ken

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