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A096559 Consecutive states of a linear congruential pseudo-random number generator that has the spectrally best primitive root for 2^31-1 as multiplier. 1
1, 62089911, 847344462, 1061653656, 1954074819, 226824280, 953102500, 1452288378, 50913524, 2133871779, 1843965925, 427233754, 195855103, 1546822229, 1652729917, 1636805220, 217994169, 1312006067, 208869911, 310792805, 675992938 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

REFERENCES

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.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Index entries for sequences related to pseudo-random numbers.

FORMULA

a(1)=1, a(n)=62089911*a(n-1) mod (2^31-1).

MAPLE

a:= proc(n) option remember; `if`(n<2, n,

irem(62089911 *a(n-1), 2147483647))

end:

seq(a(n), n=1..30); # Alois P. Heinz, Jun 10 2014

PROG

(PARI) a(n)=lift(Mod(62089911, 2147483647)^(n-1)) \\ M. F. Hasler, May 14 2015

CROSSREFS

Cf. A096550-A096561, A061364.

Sequence in context: A104931 A210298 A204883 * A203943 A125063 A205658

Adjacent sequences: A096556 A096557 A096558 * A096560 A096561 A096562

KEYWORD

nonn

AUTHOR

Hugo Pfoertner, Aug 14 2004

STATUS

approved

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Last modified November 28 05:56 EST 2022. Contains 358407 sequences. (Running on oeis4.)