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Impossible? by Julian Havil

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Chapter 16

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BENFORD’S LAW

Major paradoxes provide food for logical thought fordecades and sometimes centuries.

Nicholas Bourbaki

First Digits

At the end of the previous chapter, with the use of the potent Weyl Equidistribution Theorem, we saw that the first digit of powers of 2 are not distributed uniformly over {1, 2, 3, . . . , 9} but rather according to the law

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Moreover, we argued that the phenomenon exists equally with 2 replaced by any number that is not a rational power of 10. Perhaps this behaviour is then a property of powers of integers, ...

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