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Search: id:A096555
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| A096555 |
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Consecutive internal states of the linear congruential pseudo-random number generator RANDU that was used in the IBM Scientific Subroutine Library for IBM System/360 computers in the 1970's. |
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+0
1
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| 1, 65539, 393225, 1769499, 7077969, 26542323, 95552217, 334432395, 1146624417, 1722371299, 14608041, 1766175739, 1875647473, 1800754131, 366148473, 1022489195, 692115265, 1392739779, 2127401289, 229749723, 1559239569
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Due to a poor choice of the multiplier the generator fails most 3-d criteria for randomness. 9*a(n-2)-6*a(n-1)+a(n) = 0 mod 2^31. This was first described by George Marsaglia. The Java applet given in the link demonstrates the deficient behavior.
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REFERENCES
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D. E. Knuth, The Art of Computer Programming Third Edition. Vol. 2 Seminumerical Algorithms. Chapter 3.3.4 The Spectral Test, Page 107. Addison-Wesley 1997.
Marsaglia G., Random numbers fall mainly in the planes, Proceedings of the National Academy of Sciences, 61, 25-28, 1968
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LINKS
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Java applet demonstrating random number generation with the Linear Congruential Method.
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FORMULA
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a(1)=1, a(n) = 65539*a(n-1) mod 2^31. The sequence is periodic with period length 2^29.
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CROSSREFS
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Cf. A096550 - A096561 for other pseudo-random number generators.
Sequence in context: A013964 A036094 A133865 this_sequence A063825 A043678 A032781
Adjacent sequences: A096552 A096553 A096554 this_sequence A096556 A096557 A096558
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KEYWORD
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nonn
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Jul 19 2004
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