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 Loops in PI (Posted on 2012-04-15)
Loop Sequences within Pi (FOUND ON THE WEB):

Dan Sikorski pointed out an interesting loop sequence within the decimal expansion of Pi.
If you search for 169, it appears at position 40. If you then search for 40, it appears at position 70. Search for 70, ... and so on.
The sequence Dan found is: 40, 70, 96, 180, 3664, 24717, 15492, 84198, 65489, 3725, 16974, 41702, 3788, 5757, 1958, 14609, 62892, 44745, 9385, 169, 40...

My remark: the position is counted from the decimal point e.g. the string "1592" is located at position 3.

Prove: Not all number strings will loop.

Comments: ( Back to comment list | You must be logged in to post comments.)
 Easy solution Comment 5 of 5 |
14 is obviously at position 1. The number 1 is also at position 1. If we start with 14, then we get 14, 1, 1, 1, 1.... Therefore, 14 will not loop.

 Posted by Math Man on 2012-05-27 21:28:20

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