The generalized serial test applied to expansions of some irrational square roots in various bases
Authors:
W. A. Beyer, N. Metropolis and J. R. Neergaard
Journal:
Math. Comp. 24 (1970), 745-747
MSC:
Primary 65.15
DOI:
https://doi.org/10.1090/S0025-5718-1970-0273773-8
MathSciNet review:
0273773
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Abstract | References | Similar Articles | Additional Information
Abstract: A brief summary is given of the application of the generalized serial test for randomness to the digits of irrational $\surd n$ in bases $t$ where $2 \leqq n,t \leqq 15$. The results are consistent, except for a few aberrations, with the hypothesis of randomness of the digits.
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I. J. Good & T. N. Gover, "The generalized serial test and the binary expansion of $\surd 2$," J. Roy. Statist. Soc. Ser. A, v. 130, 1967, pp. 102–107.
I. J. Good & T. N. Gover, "Corrigendum," J. Roy. Statist. Soc. Ser. A, v. 131, 1968, p. 434.
W. A. Beyer, N. Metropolis & J. R. Neergaard, "Square roots of integers 2 to 15 in various bases 2 to 10: 88062 binary digits or equivalent," Math. Comp., v. 23, 1969, p. 679. RMT 45.
- W. A. Beyer, N. Metropolis, and J. R. Neergaard, Statistical study of digits of some square roots of integers in various bases, Math. Comp. 24 (1970), 455–473. MR 272129, DOI https://doi.org/10.1090/S0025-5718-1970-0272129-1 C. J. Everett & N. Metropolis, "Approximation of the $v$th root of N," Discrete Mathematics. (To appear.)
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Additional Information
Keywords:
Serial test,
generalized serial test,
statistics of square-root digits,
square roots,
square roots in several bases,
expansions of square roots,
random sequences,
statistical study of digit sequences
Article copyright:
© Copyright 1970
American Mathematical Society
