A384082 Consecutive states of the linear congruential pseudo-random number generator (61*s+323) mod 500 when started at s=1.

1, 384, 247, 390, 113, 216, 499, 262, 305, 428, 431, 114, 277, 220, 243, 146, 229, 292, 135, 58, 361, 344, 307, 50, 373, 76, 459, 322, 465, 188, 291, 74, 337, 380, 3, 6, 189, 352, 295, 318, 221, 304, 367, 210, 133, 436, 419, 382, 125, 448, 151, 34, 397, 40

Offset: 1

Author

Sean A. Irvine, May 18 2025

Keywords

• nonn
• easy

Comments

Periodic with period length 500.

Originally defined by Lamie in the form (61*s+2323) mod 500, even though 2323 > 500.

References

• Edward L. Lamie, Pascal Programming, John Wiley and Sons, 1987 (see p. 150).

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..500
• Stephen K. Park and Keith W. Miller, Random number generators: good ones are hard to find, Communications of the ACM, Vol 31, 10 (1988), 192-201.
• Index entries for sequences related to pseudo-random numbers.
• Index entries for linear recurrences with constant coefficients, order 500.

Crossrefs

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

Programs

Maple

a:= proc(n) option remember; `if`(n<2, n,
      irem(61*a(n-1)+323, 500))
    end:
seq(a(n), n=1..54);  # Alois P. Heinz, May 21 2025

Mathematica

NestList[Mod[61*# + 323, 500] &, 1, 100] (* Paolo Xausa, May 19 2025 *)

Formula

a(n) = (61*a(n-1) + 323) mod 500.