A384113 Consecutive states of a linear congruential pseudo-random number generator for MacModula-2 when started at 1.

1, 13, 169, 2197, 829, 1533, 1441, 245, 874, 2118, 2113, 2048, 1203, 1773, 2250, 1518, 1246, 21, 273, 1238, 2228, 1232, 2150, 218, 523, 2177, 569, 464, 1410, 2153, 257, 1030, 1835, 745, 441, 1111, 577, 568, 451, 1241, 2267, 1739, 1808, 394, 500, 1878, 1304

Offset: 1

Author

Sean A. Irvine, May 19 2025

Keywords

• nonn
• easy

Comments

An example of a terrible random number generator.

Periodic with period 1155 (well below the modulus 2311).

References

• Modula Corporation, MacModula-2 System Reference Manual, 1985 (see p. 41).

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..1155
• 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 1155.

Crossrefs

Cf. A001022.

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

Cf. A383809 (another generator with a similar problem).

Programs

Maple

a:= proc(n) option remember; `if`(n<2, n,
      irem(13*a(n-1), 2311))
    end:
seq(a(n), n=1..47);  # Alois P. Heinz, May 21 2025

Mathematica

NestList[Mod[13*#, 2311] &, 1, 100] (* Paolo Xausa, May 22 2025 *)

PARI

my(f=Mod(13,2311)); a(n) = lift(f^((n-1) % 1155)); \\ Kevin Ryde, May 25 2025

Formula

a(n) = 13 * a(n-1) mod 2311.