

A096559


Consecutive states of a linear congruential pseudorandom number generator that has the spectrally best primitive root for 2^311 as multiplier.


1



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

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 2^311. SIAM Journal on Scientific and Statistical Computing, Volume 7, Issue 1 (1986), 2445. 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. AddisonWesley 1997.


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Index entries for sequences related to pseudorandom numbers.


FORMULA

a(1)=1, a(n)=62089911*a(n1) mod (2^311).


MAPLE

a:= proc(n) option remember; `if`(n<2, n,
irem(62089911 *a(n1), 2147483647))
end:
seq(a(n), n=1..30); # Alois P. Heinz, Jun 10 2014


PROG

(PARI) a(n)=lift(Mod(62089911, 2147483647)^(n1)) \\ M. F. Hasler, May 14 2015


CROSSREFS

Cf. A096550A096561, 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



