A384779 Consecutive states of the linear congruential pseudo-random number generator 68909602460261*s mod 2^48 when started at 1.

1, 68909602460261, 267986871311321, 40223525715613, 170906480868849, 105934630117909, 220872133340233, 58531276790477, 54428804463841, 144397689558725, 44956117505465, 810057454589, 86145210100945, 204213264588917, 259238501435433, 238216607930925

Offset: 1

Author

Sean A. Irvine, Jun 09 2025

Keywords

• nonn
• easy

Comments

Periodic with period 2^46.

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.
• Index entries for sequences related to pseudo-random numbers.

Crossrefs

Cf. A384696, A384746, A384775, A384776, A384778, A384780.

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

Programs

Maple

a:= proc(n) option remember; `if`(n<2, n,
      irem(68909602460261*a(n-1), 2^48))
    end:
seq(a(n), n=1..16);  # Alois P. Heinz, Jun 09 2025

Mathematica

NestList[Mod[68909602460261*#, 2^48] &, 1, 30] (* Paolo Xausa, Jun 11 2025 *)

Formula

a(n) = 68909602460261 * a(n-1) mod 2^48.