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A096559
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Consecutive states of a linear congruential pseudo-random number generator that has the spectrally best primitive root for 2^31-1 as multiplier.
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1
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1, 62089911, 847344462, 1061653656, 1954074819, 226824280, 953102500, 1452288378, 50913524, 2133871779, 1843965925, 427233754, 195855103, 1546822229, 1652729917, 1636805220, 217994169, 1312006067, 208869911, 310792805, 675992938
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OFFSET
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1,2
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COMMENTS
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The results of the spectral tests for this generator are given in line 18 of Table 1 in D. Knuth's TAOCP vol. 2, page 106.
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REFERENCES
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G. A. Fishman, L. R. Moore III; An exhaustive analysis of multiplicative congruential random number generators with modulus 2^31-1. SIAM Journal on Scientific and Statistical Computing, Volume 7, Issue 1 (1986), 24-45. Erratum, ibid, Vol. 7, Issue 3 (1986) p. 1058
D. E. Knuth, The Art of Computer Programming Third Edition. Vol. 2 Seminumerical Algorithms. Chapter 3.3.4 The Spectral Test, Page 108. Addison-Wesley 1997.
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LINKS
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FORMULA
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a(1)=1, a(n)=62089911*a(n-1) mod (2^31-1).
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MAPLE
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a:= proc(n) option remember; `if`(n<2, n,
irem(62089911 *a(n-1), 2147483647))
end:
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PROG
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(PARI) a(n)=lift(Mod(62089911, 2147483647)^(n-1)) \\ M. F. Hasler, May 14 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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