A384637 Consecutive states of the linear congruential pseudo-random number generator 5^13*s mod 2^35 when started at s=1.

1, 1220703125, 30903841977, 6589172397, 2335288753, 33236884229, 14113929449, 5184031389, 9287939169, 11535683445, 23833284121, 2547937165, 6466389009, 29109403877, 12213593161, 31057406333, 2513210561, 12977872725, 17811893113, 2710136941, 28076457585

Offset

1,2

Comments

Periodic with period 2^33.

References

W. C. Bulnren, Discrete System Simulation, Prentice-Hall, 1982 (see p. 155).

Links

Sean A. Irvine, Table of n, a(n) for n = 1..10000

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.

Formula

a(n) = 5^13*a(n-1) mod 2^35.

Mathematica

a[1] = 1; a[n_] := a[n] = Mod[5^13*a[n - 1], 2^35]; Array[a, 21] (* Shenghui Yang, Jun 06 2025 *)

Prog

(Python)
def a(n):
    m = 1 << 35
    return pow(5**13, n, m) # Darío Clavijo, Jun 05 2025

Crossrefs

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

Sequence in context: A346362 A119333 A309227 * A195988 A262996 A022250

Adjacent sequences: A384634 A384635 A384636 * A384638 A384639 A384640

Keyword

nonn,easy

Author

Sean A. Irvine, Jun 05 2025

Status

approved