I noticed that there are some odd looping numbers in pi(adsbygoogle = window.adsbygoogle || []).push({});

Following the rule that : the string becomes the position which becomes the string ( I'll use " Sn " for string number and " Pn " for position number, ( after the decimal ) becomes the next string to locate ( Sn → Pn → Sn )

The process is easy, you start with the number and find it's position in pi digits, the position of the number becomes the next string to search for.

For smaller numbers, ( excluding the self-locating digit 1 ) most of these series grow rapidly, however, certain numbers, like 16, 19, 23, 37, 40, 169, will loop on themselves following the rule of Sn → Pn → Sn

So far I have found that

19 loops on 37 ( 19*37 is a also a figurate triangular number )

16 and 23 loop on 40

169 loops on 40

37 and 40 loop back to themselves

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37 → 46 → 19 → 37 →∞

40 →70 →96 → 180 →3664 →24717 → 15492 → 84198 → 65489 →3725 → 16974 → 41702 → 3788 → 5757 → 1958 →14609 →62892 → 44745→ 9385 →169 →40→∞

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So, does this mean that the above two series { 40 → ... 40 → } and { 37 → 37 } contains all looping numbers ?

What is the reason for this phenomenon in pi digits ?

How many numbers are there that will do this in pi ?

Thanks :)

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# Looping numbers in pi

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