A384696 Consecutive states of the linear congruential pseudo-random number generator Cray RANF when started at 1.

1, 44485709377909, 232253848878969, 94800993741645, 243522309605169, 20783065360997, 154093299791145, 161954398135485, 183663036741473, 207319719370837, 142356556532697, 278312552510253, 242082341486737, 37630394630981, 176334633251721, 233894773868189

Offset

1,2

Comments

Periodic with period 2^46.

Also implemented in the GNU Scientific Library as gsl_rng_ranf.

Also implemented in PASCLIB for Pascal programs on the CDC Cyber computers.

Links

Sean A. Irvine, 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.

Mark Galassi, Jim Davies, James Theiler, Brian Gough, Gerard Jungman, Michael Booth, and Fabrice Rossi, GNU Scientific Library: Reference Manual, 2003 (see p. 181).

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

Index entries for sequences related to pseudo-random numbers.

Formula

a(n) = 44485709377909 * a(n-1) mod 2^48.

Maple

a:= proc(n) option remember; `if`(n<2, n,
      irem(44485709377909*a(n-1), 2^48))
    end:
seq(a(n), n=1..16);  # Alois P. Heinz, Jun 09 2025

Mathematica

NestList[Mod[44485709377909*#, 2^48] &, 1, 30] (* Paolo Xausa, Jun 11 2025 *)

Crossrefs

Cf. A384746, A384775, A384776, A384778, A384779, A384780.

Cf. A384546, A384547, A384548, A384549, A384550, A384551, A384552

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

Sequence in context: A211112 A132389 A384776 * A186913 A262193 A219320

Adjacent sequences: A384693 A384694 A384695 * A384697 A384698 A384699

Keyword

nonn,easy

Author

Sean A. Irvine, Jun 07 2025

Status

approved