A385080 Consecutive states of the linear congruential pseudo-random number generator 237*s mod (2^16+1) when started at s=1.

1, 237, 56169, 8042, 5381, 30094, 54282, 19582, 53344, 59424, 58570, 52783, 57541, 5521, 63274, 53502, 31333, 20240, 12679, 55758, 41709, 54483, 1682, 5412, 37441, 26022, 6736, 23544, 9283, 37350, 4455, 7243, 12629, 43908, 51350, 45605, 60317, 8063, 10358

Offset

1,2

Comments

Periodic with period 2^16.

Attributed by Sharp and Bays to L. Afflerbach.

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 65536.

Formula

a(n) = 237 * a(n-1) mod (2^16+1).

Maple

a:= proc(n) option remember; `if`(n<2, n,
      irem(237*a(n-1), 65537))
    end:
seq(a(n), n=1..44);  # after Alois P. Heinz

Mathematica

NestList[Mod[237*#, 65537] &, 1, 50] (* Paolo Xausa, Jun 17 2025 *)

Prog

(PARI) a(n) = lift(Mod(237, 65537)^(n-1)) \\ Jianing Song, Jun 17 2025

Crossrefs

Cf. A385079.

Sequence in context: A256805 A192283 A069420 * A205068 A229077 A129124

Adjacent sequences: A385077 A385078 A385079 * A385081 A385082 A385083

Keyword

nonn,easy

Author

Sean A. Irvine, Jun 16 2025

Status

approved