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.**