One of my interests in pi, and this is all purely recreational, is locating unique integers/relationships, looping numbers ( " orbits " ) etc.(adsbygoogle = window.adsbygoogle || []).push({});

Inpi, certain integers are located with a position number that when multiplied, by single integers, will return the number itself as a product.

For example, the square of 12:

{ ...77235014144197356854... }: 144 at the 1638th position

1*6*3*8 = 144

My question is this:

Is there a simple way to determine which integers have this relationship with their position numbers, in pi ?

I already know I can disregard any position number with 0 as a digit, as it will give 0 as a product.

As a string grows larger, say instead of a 3 digit integer like 144, I search for an 8 digit integer, like 14444444, the frequency with which the string occurs, becomes less and less frequent,

..so is it reasonable to assume that the probability of finding that particular relationship between a string and the multiplicative product of it's position number, becomes less and less probable as the string grows larger ?

How would this apply for pi in other bases, if at all ?

Thanks,

Isaac

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# Question about strings in pi

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