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Normal numbers

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A real number is said to be simply normal to base b[1] if its sequence of [base b] digits is asymptotically uniformly distributed, in the sense that each of the b digit values has the same natural density 1/b, also all possible b2 pairs of digits are equally likely with density b−2, all b3 triplets of digits equally likely with density b−3, etc.

A normal number (absolutely normal number) is a real number which happens to be simply normal to every base b.[1] Thus, the set of normal numbers is the intersection, for all bases b,[1] of the set of base b simply normal numbers.


  1. 1.0 1.1 1.2 The only bases considered here are natural numbers greater than 1.