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# Normal numbers

From OeisWiki

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 `b`^{2} pairs of digits are equally likely with density `b`^{−2}, all `b`^{3} 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.

## Notes

- ↑
^{1.0}^{1.1}^{1.2}The only bases considered here are natural numbers greater than 1.