A357907 The output of a Sinclair ZX81 random number generator.

1, 149, 11249, 57305, 38044, 35283, 24819, 26463, 18689, 25472, 9901, 21742, 57836, 12332, 7456, 34978, 1944, 14800, 61482, 23634, 3125, 37838, 19833, 45735, 22275, 32274, 61292, 9384, 48504, 33339, 10093, 36142, 23707, 8600, 55241, 14318, 25332, 64938, 20686, 44173, 36199, 27982

Offset

1,2

Comments

The ZX81 had a congruential random number generator with the hardcoded values: x <- (75*x + 74) mod 65537.

This sequence starts with x = 1. The ZX81 had the option to start with a hardware counter.

The sequence has period 2^16. - Rémy Sigrist, Oct 20 2022

Links

Jianing Song, Table of n, a(n) for n = 1..65536

Wikipedia, Linear congruential generator.

Index entries for linear recurrences with constant coefficients, order 32769.

Index entries for sequences related to pseudo-random numbers.

Formula

a(n) = (75*a(n-1) + 74) mod 65537, a(1) = 1.

a(n + 2^16) = a(n). - Rémy Sigrist, Oct 20 2022

a(n) = (2*75^(n-1) - 1) mod 65537. - Kevin Ryde, Oct 20 2022

a(n) = a(n-1) - a(n-32768) + a(n-32769) for n > 32769. - Ray Chandler, Aug 03 2023

Mathematica

NestList[Mod[75*# + 74, 65537] &, 1, 50] (* Paolo Xausa, Oct 03 2024 *)

Prog

(R)
x <- 1
nxt <- function(x) (75*x + 74) %% 65537
for (t in 1:1000) {
  cat(sprintf('%i, ', x))
  x <- nxt(x)
}
(PARI) my(c=Mod(75, 65537)); a(n) = lift(2*c^(n-1) - 1); \\ Kevin Ryde, Oct 22 2022
(Python)
def a(n): return (2*pow(75, n-1, 65537) - 1)%65537
print([a(n) for n in range(1, 43)]) # Michael S. Branicky, Oct 23 2022

Crossrefs

Cf. A061364, A096550-A096561, A260083, A276820.

Sequence in context: A158717 A243530 A219081 * A359403 A188566 A188753

Adjacent sequences: A357904 A357905 A357906 * A357908 A357909 A357910

Keyword

nonn,easy

Author

Jacques Basaldúa, Oct 19 2022

Status

approved