A384775 Consecutive states of the linear congruential pseudo-random number generator 33952834046453*s mod 2^48 when started at 1.

1, 33952834046453, 181226512753785, 17547632994509, 138001340383537, 86153482263781, 229799995061289, 280681352600637, 119513974041441, 216025667693781, 238363414258905, 47318339740845, 113868956675729, 85138704755141, 217581192963721, 88846792569373

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, A384776, A384778, A384779, A384780.

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

Programs

Maple

a:= proc(n) option remember; `if`(n<2, n,
      irem(33952834046453*a(n-1), 2^48))
    end:
seq(a(n), n=1..16);  # Alois P. Heinz, Jun 09 2025

Mathematica

NestList[Mod[33952834046453*#, 2^48] &, 1, 30] (* Paolo Xausa, Jun 11 2025 *)

Formula

a(n) = 33952834046453 * a(n-1) mod 2^48.