Champernowne's Number, Strong Normality, and the X Chromosome
نویسندگان
چکیده
Champernowne’s number is the best-known example of a normal number, but its digits are far from random. The sequence of nucleotides in the human X-chromosome appears non-random in a similar way. We give a new test of pseudorandomness, strong normality, based on the law of the iterated logarithm. Almost all numbers are strongly normal, and we show that a strongly normal number must necessarily be normal. However, Champernowne’s number fails to be strongly normal. This paper is dedicated to Jon Borwein in celebration of his 60th birthday.
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