If there's an error, however, please notify me by emailing dga - at - pobox DOT com and I'll upgrade.
You can find the source code to the pi searcher here in tar. If we view Pi as a big, random string of numbers which is close enough for our purposes , then we can figure out the odds of finding any string in the first million digits of Pi:.
The Pi-Search Page
I've also posted a more in-depth explanation of the probability of finding strings in Pi for people who are curious. Pi contains a few self-locating strings, but not many. Defining self-locating depends how you count the "position". If you treat the first digit after the decimal point as digit "1" which the pi searcher does , then you get the following numbers which can self-locate themselves in the first M digits of pi:.
If, on the other hand, you act like a computer geek and use zero based indexing, then you get these numbers:. If you disregard either of the ending twos, you find that it's the same position at which you find Ahh, the palindromic possibilities inherent in a reversible meaning of life string.
He found 9 6's at , 9 7's at and 9 8's at There are also the above mentioned 42's. Can you find something else? Many thanks to Carola Schermuly, who prompted me to figure out a most useless but interesting bit of Pi trivia: The maximum number of digits of Pi necessary to find any month-day combination is Interestingly enough, this is the same value with European date formats meaning March 12th and American date formats - the same date, December 3rd, is the winner.
It takes digits after the decimal point to find them.
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Dan Sikorski pointed out an interesting loop sequence within Pi. If you search for , it appears at position If you then search for 40, it appears at position Search for 70, The sequence Dan found is: 40, 70, 96, , , , , , , , , , , , , , , , , , One has to wonder: What is the probability of finding a loop for any given initial search string? Or even, within the infinite expansion of pi, would all searches necessarily fall into a loop? The expected number of digits required to find a search string is proportional to the length of the string, but the requirement to loop again makes the analysis a bit tricky.
Anyone know? Doug Hafen points out that that not all numbers will loop because of the self-locating strings. It's also possible to drop into a self-locating string, e. No loop. Thanks, Doug!
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Results The string occurs at position. Find Next The string and surrounding digits: text version - beta! About the odds of finding or not finding your number in Pi. Share on Twitter. News [ more ] Huge overhaul: The pi searcher is now interactive. Pi stuff - shirts, mugs, books show your love of Pi!
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