A385039 Consecutive internal states of the linear congruential pseudo-random number generator (171*s + 11213) mod 53125 when started at 1.

1, 11384, 45377, 14430, 34993, 45016, 5824, 50867, 50095, 24333, 28406, 34264, 26607, 45385, 15798, 3296, 43579, 25722, 300, 9388, 22811, 33769, 48212, 21090, 5103, 33826, 4834, 40952, 1505, 2943, 36341, 9899, 3942, 47795, 2908, 30356, 48964, 43432, 585, 4998

Offset: 1

Author

Sean A. Irvine, Jun 13 2025

Keywords

• nonn
• easy

Comments

Periodic with period 53125.

Described in Numerical Recipes as a "quick and dirty" generator.

References

• William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery, Numerical Recipes in C (2nd ed), Cambridge University Press, 1999 (see p. 285).

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..10000
• 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 53125.

Crossrefs

Cf. A384113, A384114, A384126, A384152, A384158, A384196.

Programs

Maple

a:= proc(n) option remember; `if`(n<2, n,
      irem(171*a(n-1)+11213, 53125))
    end:
seq(a(n), n=1..45);  # after Alois P. Heinz

Mathematica

NestList[Mod[171*# + 11213, 53125] &, 1, 50] (* Paolo Xausa, Jun 16 2025 *)

Formula

a(n) = (171*a(n-1) + 11213) mod 53125.