A096561 - OEIS

A096561

Consecutive internal states of the second of the two linear congruential random number generators whose combined output is used in function RANDOM_NUMBER in version 8 of the Intel FORTRAN Compiler for Linux, using its intrinsic initialization.

2147483398, 2147442707, 491644535, 44073136, 275411947, 1494571342, 367188984, 1612130085, 1622029567, 724872099, 810967243, 1649143122, 223185073, 139696145, 126975187, 29251410, 592572674, 1023646436, 1632766708, 1701483674, 1908878648, 1615402586, 1642669521

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OFFSET

1,1

COMMENTS

This is part 2 of a combined pseudorandom number generator proposed by Pierre L'Ecuyer. For more information, references and links see A096560. For the spectral properties see Table 1, line 21, on page 106 of Knuth's TAOCP Vol. 2.

This sequence has period 2^31 - 250. - Charles R Greathouse IV, Sep 10 2015

REFERENCES

P. L'Ecuyer, Efficient and portable combined random number generators, Communications of the ACM, v.31 n.6, p. 742-751 and 774, 1988.

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 periodic sequences with large period.

Index entries for sequences related to pseudo-random numbers.

FORMULA

a(1)=2^31-250, a(n)=40692*a(n-1) mod (2^31-249).

MAPLE

a:= proc(n) option remember; `if`(n=1, 2147483398,

irem(40692 *a(n-1), 2147483399))

end:

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

MATHEMATICA