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), 745747
MSC:
Primary 65.15
DOI:
https://doi.org/10.1090/S00255718197002737738
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.

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/S00255718197002721291 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 squareroot 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