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

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

NestList[Mod[#*40692, 2^31 - 249] &, 2^31 - 250, 50] (* Paolo Xausa, Aug 29 2024 *)

Prog

(PARI) a(n)=lift(-Mod(40692, 2147483399)^(n-1)) \\ M. F. Hasler, May 14 2015

Crossrefs

Cf. A096550-A096560, A061364.

Sequence in context: A292546 A287593 A216012 * A096560 A011581 A200526

Adjacent sequences: A096558 A096559 A096560 * A096562 A096563 A096564

Keyword

nonn,easy

Author

Hugo Pfoertner, Aug 13 2004

Status

approved