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

1,2

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.

Formula

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

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

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 *)

Crossrefs

Cf. A384159, A384160.

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

Sequence in context: A271985 A391913 A255182 * A176087 A006060 A077695

Adjacent sequences: A384155 A384156 A384157 * A384159 A384160 A384161

Keyword

nonn,easy

Author

Sean A. Irvine, May 20 2025

Status

approved