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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
MathSciNet review: 0273773
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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.

References [Enhancements On Off] (What's this?)

  • [1] 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.
  • [2] I. J. Good & T. N. Gover, "Corrigendum," J. Roy. Statist. Soc. Ser. A, v. 131, 1968, p. 434.
  • [3] 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.
  • [4] W. A. Beyer, N. Metropolis & J. R. Neergaard, "Statistical study of digits of some square roots of integers in various bases," Math. Comp., v. 24, 1970, pp. 455-473. MR 0272129 (42:7010)
  • [5] C. J. Everett & N. Metropolis, "Approximation of the $ v$th root of N," Discrete Mathematics. (To appear.)

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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

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