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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.

%I A096559 #23 Aug 29 2024 11:56:27
%S A096559 1,62089911,847344462,1061653656,1954074819,226824280,953102500,
%T A096559 1452288378,50913524,2133871779,1843965925,427233754,195855103,
%U A096559 1546822229,1652729917,1636805220,217994169,1312006067,208869911,310792805,675992938,1109700100,855351136,863373758
%N A096559 Consecutive states of a linear congruential pseudo-random number generator that has the spectrally best primitive root for 2^31-1 as multiplier.
%C A096559 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.
%D A096559 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 A096559 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.
%H A096559 Alois P. Heinz, <a href="/A096559/b096559.txt">Table of n, a(n) for n = 1..10000</a>
%H A096559 <a href="/index/Ps#PRN">Index entries for sequences related to pseudo-random numbers</a>.
%F A096559 a(1)=1, a(n)=62089911*a(n-1) mod (2^31-1).
%p A096559 a:= proc(n) option remember; `if`(n<2, n,
%p A096559       irem(62089911 *a(n-1), 2147483647))
%p A096559     end:
%p A096559 seq(a(n), n=1..30);  # _Alois P. Heinz_, Jun 10 2014
%t A096559 NestList[Mod[#*62089911, 2^31 - 1] &, 1, 50] (* _Paolo Xausa_, Aug 29 2024 *)
%o A096559 (PARI) a(n)=lift(Mod(62089911,2147483647)^(n-1)) \\ _M. F. Hasler_, May 14 2015
%Y A096559 Cf. A096550-A096561, A061364.
%K A096559 nonn
%O A096559 1,2
%A A096559 _Hugo Pfoertner_, Aug 14 2004