A096559 - OEIS

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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, 62089911, 847344462, 1061653656, 1954074819, 226824280, 953102500, 1452288378, 50913524, 2133871779, 1843965925, 427233754, 195855103, 1546822229, 1652729917, 1636805220, 217994169, 1312006067, 208869911, 310792805, 675992938, 1109700100, 855351136, 863373758

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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

MATHEMATICA

NestList[Mod[#*62089911, 2^31 - 1] &, 1, 50] (* Paolo Xausa, Aug 29 2024 *)