Re: Arbitrary strings of digits in the decimal display of Pi

From: Edwin Clark (eclark_at_math.usf.edu)
Date: 09/23/04 

Date: Thu, 23 Sep 2004 21:10:05 GMT

Carl Devore wrote:
> On Tue, 21 Sep 2004, J.Barsuhn wrote:
>
>>What I would be interested especially is whether some of the irrational
>>numbers a beginning student would hit have this property (of containing
>>any previously defined sequence of digits somewhere in its decimal
>>representation): Numbers like sqrt(2) or the Euler e. If I interpret
>>Carlīs (Devore) posting correctly, he says yes.
>
>
> It would be a good exercise for the beginning CAS student to write a
> program to find the position of the first occurence of digit string d in
> irrational alpha.

At the website http://pi.nersc.gov/ you can search the first four
billion binary digits of Pi for a string. For example my first name
edwin (encodes into binary by the website) yields:

search string = "edwin"
25-bit binary equivalent = 0010100100101110100101110

search string found at binary index = 2983683776

This was discussed a few years ago (probably on sci.math) and people had
fun finding things in pi. Some interesting facts about the distribution
of the first four billion binary digits of Pi are given at the site.

There you will also find a link to a paper by Bailey and Crandall that
proves normality for a certain class of numbers.

Edwin