Re: Randomness of digits within pi

On 9 Nov, 16:22, "G.E. Ivey" <george.i...@xxxxxxxxxxxxx> wrote:
On 9 Nov, 12:53, "George Marsaglia"
<g...@xxxxxxxxxxxx> wrote:
<jonas.thornv...@xxxxxxxxxxx> wrote in message

news:1194606172.590463.231420@xxxxxxxxxxxxxxxxxxxxxxxx
com...

On 9 Nov, 11:53, jankri...@xxxxxxxxxxx wrote:
On 9 Nov, 11:41, jonas.thornv...@xxxxxxxxxxx
wrote:

When i was playing around at
"http://zenwerx.com/pi.phplooking"; for
occurences of my personalnumber within PI i
noticed that 333333 and
especially 666666 do not seem to occur as
frequent as

111111,222222,444444,555555,777777,888888,999999 or
XXXXXX (without
testing all ;)

Is this just a fluke result of to small sample
size at the page, could
anyone verify searching in the big file with a
program?

If that really the case that 333333 andd
666666 is a lot less frequent
what is the mathematical reason?

J

If there are 4 million digits, that's a sample
size that is far too
small to say anything about the frequency of
111111 and the others.
Each of them should only turn up once in one
million digits on
average.

---
J K Hauglandhttp://home.no.net/zamunda

Yes i thought the downloadable sample file was
bigger but i can see it
is same size now.
But what is known about the distribution of
larger digits
(numberstrings?) within pi, is it really randomed
distributed?

So i try again is six digit numbers randomly
distributed within pi, if
not why?

J

The pdf article

interstat.statjournals.net/YEAR/2005/articles/0510005.
pdf

describes results from a number of tests on the
randomness
of the digits of pi, as well as e, sqrt(2) and the
decimal
expansions of various rationals.

A related article,

interstat.statjournals.net/YEAR/2006/articles/0601001.
pdf

refutes claims from Physicists at Purdue that the
digits
of pi are not as random as those from other
sources.

George Marsaglia- D?lj citerad text -

- Visa citerad text -

Maybe but for sure it is an interesting fact that two
strings of
"7777777" turns up in just a sample of 4 million and
that "666666"
only occur one time in 4 million digits.

No, it's not at all interesting! As Jan Kristian Haugland told you in the very first response to you post "Each of them should only >turn up once in one million digits on average." So might expect only 4 occurrances of ANY 6 digit number in 4 million >digits. Occuring one or two times when the expected value is only 4 is not interesting at all.

So it is just a fluke for 7 billion number "7777777" to turn up 2 two
times in the first 4 million of digits?

Could you be so kind to direct me to a file with the decimal expansion
of pi it would be nice with at least 100 million digits, that would be
a file of 800 MB and i am sure many of us have the space.

So we can research the properties of pi on our own, i do not know if
the there still is a 4GB file size limit for files in Windows, but 400
million digits would be nice if anyone have.

Of course if there is a fast algorithm to generate the first 400
million numbers even better, i do not have any compiler installed so a
executional file would be nice.

J


J- Dölj citerad text -

- Visa citerad text -- Dölj citerad text -

- Visa citerad text -


.

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