A384780 Consecutive states of the linear congruential pseudo-random number generator 127107890972165*s mod 2^48 when started at 1.

1, 127107890972165, 97936613129241, 273514721657469, 208157768792689, 190871074753077, 130077535940873, 140242115373869, 12589906159073, 144775771571045, 83191635750649, 67018942496989, 27094905090641, 40503495991701, 211801672787433, 25600309900173

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, A384779.

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

Programs

Maple

a:= proc(n) option remember; `if`(n<2, n,
      irem(127107890972165*a(n-1), 2^48))
    end:
seq(a(n), n=1..16);  # Alois P. Heinz, Jun 09 2025

Mathematica

NestList[Mod[127107890972165*#, 2^48] &, 1, 30] (* Paolo Xausa, Jun 11 2025 *)

Formula

a(n) = 127107890972165 * a(n-1) mod 2^48.