A384152 Consecutive states of the linear congruential pseudo-random number generator used by OMNITAB II when started at 1.

1, 125, 7433, 3429, 2641, 2445, 2521, 3829, 3489, 1949, 6057, 3461, 6641, 2733, 5753, 6421, 8001, 701, 5705, 421, 3473, 8141, 1817, 5941, 5345, 4573, 6377, 2501, 1329, 2285, 7097, 2389, 3713, 5373, 8073, 1509, 209, 1549, 5209, 3957, 3105, 3101, 2601, 5637, 113

Offset: 1

Author

Sean A. Irvine, May 20 2025

Keywords

• nonn
• easy

Comments

Periodic with period length 2048.

A terrible generator with period much less than the modulus.

Also, RN5 of the IRCCRAND package.

Originally defined by Kruskal including the implementation s = 5*s mod 8192; s = 5*s mod 8192; s = 5*s mod 8192 (rather than s = 125*s mod 8192).

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..2048
• Edward J. Dudewicz, IRCCRAND - The Ohio State University Random Number Generator Package, Technical Report, 1974.
• David Hogben, Sally T. Peavy, and Ruth N. Varner, OMNITAB II: User's Reference Manual, NBS Technical Note 552, 1971.
• J. B. Kruskal, Extremely portable random number generator, Communications of the ACM, 12, 2 (1969), 93-94.
• W. E. Sharp and Carter Bays, A review of portable random number generators, Computers and Geosciences, 18, 1 (1982), 79-87.
• Index entries for sequences related to pseudo-random numbers.
• Index entries for linear recurrences with constant coefficients, order 2048.

Crossrefs

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

Cf. A383809, A384113, A384126, A384971, A384973 (other examples with short periods).

Programs

Maple

a:= proc(n) option remember; `if`(n<2, n,
      irem(125*a(n-1), 2^13))
    end:
seq(a(n), n=1..45);  # Alois P. Heinz, May 21 2025

Mathematica

NestList[Mod[125*#, 2^13] &, 1, 100] (* Paolo Xausa, May 21 2025 *)

PARI

a(n) = lift(Mod(5,8192)^(3*n-3)) \\ Jianing Song, Jul 06 2025

Formula

a(n) = 125 * a(n-1) mod 2^13.