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Statistical Study of Digits of Some Square Roots of Integers in Various Bases

1970
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Mathematics of Computation
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Some statistical tests of randomness are made of the first 88062 binary digits (or equivalent in other bases) of Jn in various bases b, 2 g n g 15 (n square-free) with b = 2,4, 8, 16 and n = 2, 3, 5 with b = 3,5, 6, 7, and 10. The statistical tests are the y2 test for cumulative frequency distribution of the digits, the lead test, and the gap test. The lead test is an examination of the distances over which the cumulative frequency of a digit exceeded its expected value. It is related to the

doi:10.2307/2004493
fatcat:b6e2w3svrnfmdgsvc4y4gmjtta