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

Author

Sean A. Irvine, Jun 07 2025

Keywords

• nonn
• easy

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.

Crossrefs

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

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

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

Programs

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 *)

Formula

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