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

Offset: 1

Author

Hugo Pfoertner, Aug 14 2004

Keywords

• nonn

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.

Crossrefs

Cf. A096550-A096561, A061364.

Programs

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 *)

PARI

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

Formula

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