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

1,2

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.

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A001022.

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

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

Sequence in context: A188869 A014956 A171287 * A045593 A045597 A045600

Adjacent sequences: A384110 A384111 A384112 * A384114 A384115 A384116

Keyword

nonn,easy

Author

Sean A. Irvine, May 19 2025

Status

approved