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The Generalized Serial Test and the Binary Expansion of $\sqrt 2$

I. J. Good and T. N. Gover
Journal of the Royal Statistical Society. Series A (General)
Vol. 130, No. 1 (1967), pp. 102-107
Published by: Wiley for the Royal Statistical Society
DOI: 10.2307/2344040
Stable URL: http://www.jstor.org/stable/2344040
Page Count: 6
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The Generalized Serial Test and the Binary Expansion of $\sqrt 2$
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Abstract

The generalized serial test is a very useful test for the randomness or pseudo-randomness of sequences, especially binary sequences. Unfortunately the test has been incorrectly used several times, and our purpose is to give a clear exposition of its correct use, with an example. The example used is the binary expansion of √ 2 to 10,000 places. Previous statistical analyses of the expansions of familiar irrational numbers have, as far as we know, been carried out exclusively for decimal expansions.

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