A383809 Consecutive states of a linear congruential pseudo-random number generator for Lisp 1985 when started at 1.

1, 17, 38, 144, 189, 201, 154, 108, 79, 88, 241, 81, 122, 66, 118, 249, 217, 175, 214, 124, 100, 194, 35, 93, 75, 20, 89, 7, 119, 15, 4, 68, 152, 74, 3, 51, 114, 181, 65, 101, 211, 73, 237, 13, 221, 243, 115, 198, 103, 245, 149, 23, 140, 121, 49, 80, 105, 28

Offset: 1

Author

Sean A. Irvine, May 17 2025

Keywords

• nonn
• easy

Comments

An example of a terrible random number generator.

Periodic with period 125 (well below the modulus of 251).

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..125
• Richard P. Gabriel, Performance and Evaluation of Lisp Systems, MIT, 1985 (see p. 140).
• 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 125.

Crossrefs

Cf. A001026.

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

Programs

Maple

a:= proc(n) option remember; `if`(n<2, n,
      irem(17*a(n-1), 251))
    end:
seq(a(n), n=1..58);  # Alois P. Heinz, May 21 2025

Mathematica

NestList[Mod[17*#, 251] &, 1, 100] (* Paolo Xausa, May 21 2025 *)

Formula

a(n) = 17 * a(n-1) mod 251.