A384778 Consecutive states of the linear congruential pseudo-random number generator 55151000561141*s mod 2^48 when started at 1.

1, 55151000561141, 29815832362105, 55100342394061, 179741519900977, 7132195055845, 74704892394537, 220210368430141, 73887840684897, 135379684698325, 280350175386841, 124994015967405, 227696133324433, 118996703729093, 242320442691209, 24065948923421

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, A384779, A384780.

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

Programs

Maple

a:= proc(n) option remember; `if`(n<2, n,
      irem(55151000561141*a(n-1), 2^48))
    end:
seq(a(n), n=1..16);  # Alois P. Heinz, Jun 09 2025

Mathematica

NestList[Mod[55151000561141*#, 2^48] &, 1, 30] (* Paolo Xausa, Jun 11 2025 *)

Formula

a(n) = 55151000561141 * a(n-1) mod 2^48.