The numbers of Pi: Are the numbers 157 in sucession somewhere
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Because pi cannot be expressed in a terminating or recurring decimal, the group 157 in that order appear somewhere in pi, because the decimal is infinitely long. Exactly where is the question. A computer program that not only generates pi to many, many decimal places can also look for sequences of digits and tell you in what position they appear. Since there are an infinite number of digits, it could take some time to find 157, but such a short sequence is likely to appear after a few thousand decimal places, just as you might expect the number 9 to appear on average once every 10 digits; or the number 26 once every 100 digits. 157 might be expected to appear once in 1000 digits. There is no guarantee, however, because pi is not a random sequence, and there will be repeated groups.

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