A384746 Consecutive states of the linear congruential pseudo-random number generator MCNP from Los Alamos when started at 1.

1, 19073486328125, 29763723208841, 187205367447973, 131230026111313, 264374031214925, 74735272014937, 31978779697717, 72377397341089, 127824407320157, 39323977335081, 168134765887429, 73951303845617, 27971537168493, 266449281326841, 41546074810965

Offset: 1

Author

Sean A. Irvine, Jun 09 2025

Keywords

• nonn
• easy

Comments

Periodic with period 2^46.

Used for Monte Carlo simulations.

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..10000
• Forrest B. Brown and Yasunobu Nagaya, The MCNP5 Random Number Generator, LA-UR-02-3782, American Nuclear Society, Winter Meeting, 2002.
• 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.
• B. D. Ripley, Thoughts on pseudorandom number generators, J of Computational and Applied Mathematics, 31, 1 (1990), 153-163.
• Index entries for sequences related to pseudo-random numbers.

Crossrefs

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

Programs

Maple

a:= proc(n) option remember; `if`(n<2, n,
      irem(5^19*a(n-1), 2^48))
    end:
seq(a(n), n=1..16);  # Alois P. Heinz, Jun 09 2025

Mathematica

NestList[Mod[5^19*#, 2^48] &, 1, 30] (* Paolo Xausa, Jun 11 2025 *)

Formula

a(n) = 5^19 * a(n-1) mod 2^48.