A096552 Consecutive internal states of the linear congruential pseudo-random number generator MTH$RANDOM that is used in the VAX VMS Library.

0, 1, 69070, 475628535, 3277404108, 772999773, 3877832058, 3821835443, 1662200408, 2044158073, 3788989926, 797919023, 2743624612, 1156259413, 1059494674, 584849259, 786050992, 3369345009, 3077427454, 1200308583, 2654771836, 1692139853, 4052415402, 1850655011

Offset

1,3

Comments

This generator is a variant of A096551.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

George S. Fishman, Multiplicative Congruential Random Number Generators with Modulus 2^beta: An Exhaustive Analysis for beta = 32 and a Partial Analysis for beta = 48, Math. Comp., 54, 189 (1990), 331-344.

B. D. Ripley, Computer Generation of Random Variables: A Tutorial, International Statistical Review, 51 (1983), 301-309.

B. D. Ripley, Thoughts on pseudorandom number generators, J of Computational and Applied Mathematics, 31, 1 (1990), 153-163.

Index entries for sequences related to pseudo-random numbers.

Formula

a(1)=0, a(n) = (69069*a(n-1)+1) mod 2^32. The sequence is periodic with period length 2^32. [Corrected based on a comment from Kevin Ryde, Nov 13 2024]

Maple

a:= proc(n) option remember; `if`(n<2, 0,
      irem(69069 *a(n-1)+1, 4294967296))
    end:
seq(a(n), n=1..30);  # Alois P. Heinz, Jun 10 2014

Mathematica

NestList[Mod[#*69069 + 1, 2^32] &, 0, 50] (* Paolo Xausa, Aug 29 2024 *)

Crossrefs

Cf. A096550-A096561 for other pseudo-random number generators.

Sequence in context: A250500 A354194 A096551 * A385127 A392226 A031663

Adjacent sequences: A096549 A096550 A096551 * A096553 A096554 A096555

Keyword

nonn

Author

Hugo Pfoertner, Jul 18 2004

Status

approved