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: A brief summary is given of the application of the generalized serial test for randomness to the digits of irrational in bases where . The results are consistent, except for a few aberrations, with the hypothesis of randomness of the digits.

**[1]**I. J. Good & T. N. Gover, "The generalized serial test and the binary expansion of ,"*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, and J. R. Neergaard,*Statistical study of digits of some square roots of integers in various bases*, Math. Comp.**24**(1970), 455–473. MR**0272129**, https://doi.org/10.1090/S0025-5718-1970-0272129-1**[5]**C. J. Everett & N. Metropolis, "Approximation of the th root of*N*,"*Discrete Mathematics*. (To appear.)

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1970-0273773-8

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