Fast growing sequences of numbers and the first digit phenomenon
Abstract
We consider a large class of fast growing sequences of numbers Un like the nth superfactorial , the nth hyperfactorial
and similar ones. We show that their mantissas are distributed following Benford's law in the sense of the natural density. We prove that this is also verified by
, by
and is passed down to all the sequences obtained by iterating this design process. We also consider the superprimorial numbers and the products of logarithms of integers.
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