A096560 Consecutive internal states of the first 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.

2147483562, 2147443549, 546363367, 801095798, 1707599834, 1415233705, 19915560, 184815967, 1440196129, 286492701, 451678520, 242633072, 2094038248, 332794338, 2034550132, 1534592081, 22528712, 1668269071, 1739534702, 1504321872, 2118598881, 1701974909, 1825258870

Offset: 1

Author

Hugo Pfoertner, Aug 13 2004

Keywords

• nonn

Comments

Comment from Raymond Wang, Oct 03 2008: (65421664*40014) mod (2^31-85) = 2^31-86.

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.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• P. L'Ecuyer, Random Number Generation, Chapter 4 of the Handbook on Simulation, Jerry Banks Ed., Wiley, 1998.
• Intel FORTRAN Language Reference, Document No. 253261-002, Chapter 9, Intrinsic Procedure RANDOM_NUMBER.
• Index entries for sequences related to pseudo-random numbers.

Crossrefs

Cf. A096561.

Programs

Maple

a:= proc(n) option remember; `if`(n=1, 2147483562,
      irem(40014 *a(n-1), 2147483563))
    end:
seq(a(n), n=1..30);  # Alois P. Heinz, Jun 10 2014

Mathematica

NestList[Mod[#*40014, 2^31 - 85] &, 2^31 - 86, 50] (* Paolo Xausa, Aug 29 2024 *)

Formula

a(1)=2^31-86, a(n)=40014*a(n-1) mod (2^31-85).