A384114 Consecutive states of the linear congruential pseudo-random number generator (125*s+1) mod 2^12 when started at s=1.

1, 126, 3463, 2796, 1341, 3786, 2211, 1944, 1337, 3286, 1151, 516, 3061, 1698, 3355, 1584, 1393, 2094, 3703, 28, 3501, 3450, 1171, 3016, 169, 646, 2927, 1332, 2661, 850, 3851, 2144, 1761, 3038, 2919, 332, 541, 2090, 3203, 3064, 2073, 1078, 3679, 1124, 1237

Offset: 1

Author

Sean A. Irvine, May 19 2025

Keywords

• nonn
• easy

Comments

Periodic with period 4096.

References

• W. F. Clocksin and C. S. Mellish, Programming in Prolog, Springer-Verlag, 1981 (see p. 149).

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..4096
• 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.
• 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 4096.

Crossrefs

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

Programs

Maple

a:= proc(n) option remember; `if`(n<2, n,
      irem(125*a(n-1)+1, 2^12))
    end:
seq(a(n), n=1..45);  # Alois P. Heinz, May 19 2025

Mathematica

a[1] = 1; a[n_] := a[n] = Mod[125*a[n - 1] + 1, 2^12]; Array[a, 45, 1] (* Shenghui Yang, May 19 2025 *)

Formula

a(n) = (125*a(n-1) + 1) mod 2^12.