A384158 Consecutive states of the linear congruential pseudo-random number generator for 16-bit WATFOR/WATFIV when started at 1.

1, 253, 31241, 6885, 5201, 5133, 20697, 26229, 16801, 23581, 2217, 3845, 22513, 26925, 29049, 9365, 10049, 19261, 23369, 14117, 32657, 4685, 5657, 22197, 12513, 20061, 29161, 4933, 2865, 3949, 16057, 31957, 24193, 25981, 19593, 9061, 31441, 24717, 27481, 5877

Offset: 1

Author

Sean A. Irvine, May 20 2025

Keywords

• nonn
• easy

Comments

Periodic with period 8192 (considerably less than the modulus).

WATFOR and WATFIV are early FORTRAN compilers from the University of Waterloo.

References

• Terry M. Walker, Fundamentals of Fortran Programming: with WATFOR/WATFIV, Allyn and Bacon, 1975.

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..8192
• Index entries for sequences related to pseudo-random numbers.
• Index entries for linear recurrences with constant coefficients, order 8192.

Crossrefs

Cf. A384159, A384160.

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

Programs

Maple

a:= proc(n) option remember; `if`(n<2, n,
      irem(253*a(n-1), 2^15))
    end:
seq(a(n), n=1..40);  # Alois P. Heinz, May 21 2025

Mathematica

NestList[Mod[253*#, 2^15] &, 1, 100] (* Paolo Xausa, May 22 2025 *)

Formula

a(n) = 253 * a(n-1) mod 2^15.

a(n) == 1 (mod 4). - Hugo Pfoertner, May 26 2025