Generating pseudo-random numbers by shuffling a Fibonacci sequence

Author:
Friedrich Gebhardt

Journal:
Math. Comp. **21** (1967), 708-709

MSC:
Primary 65.15

DOI:
https://doi.org/10.1090/S0025-5718-1967-0223064-6

MathSciNet review:
0223064

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Abstract: M. D. MacLaren and G. Marsaglia [2] have proposed to mix two pseudo-random number generators in the following way: The first generator is used at the beginning to fill an array with pseudo-random numbers; whenever a random number is needed, the second generator determines which element of the array is to be used and replaced by a new number from the first generator. In this study, only one generator is utilized for both purposes; moreover, the generator chosen (a Fibonacci sequence) is by itself a rather poor one. Nevertheless, the final sequence of pseudo-random numbers passed all statistical tests applied to it, including tests of the maximum and minimum of two to ten succeeding numbers and tests applied to sequences immediately following a small number or two almost equal ones.

**[1]**M. Greenberger, "Method in randomness,"*Comm. ACM*, v. 8, 1965, pp. 177-179.**[2]**M. D. MacLaren & G. Marsaglia, "Uniform random number generators,"*J. Assoc. Comput. Mach.*, v. 12, 1965, pp. 83-89. MR**30**#687. MR**0170449 (30:687)****[3]**D. D. Wall, "Fibonacci series modulo m,"*Amer. Math. Monthly*, v. 67, 1960, pp. 525-532. MR**22**#10945. MR**0120188 (22:10945)**

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DOI:
https://doi.org/10.1090/S0025-5718-1967-0223064-6

Article copyright:
© Copyright 1967
American Mathematical Society