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

Author

Hugo Pfoertner, Aug 13 2004

Keywords

• nonn
• easy

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

• 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
• Pierre L'Ecuyer, Efficient and portable combined random number generators, Commun. ACM, 31, 6 (1988), 742-749 and 774.
• Index entries for periodic sequences with large period.
• Index entries for sequences related to pseudo-random numbers.

Crossrefs

Cf. A096550-A096560, A061364.

Programs

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 *)

PARI

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

Formula

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