randu: Random Numbers from Congruential Generator RANDU

randuR Documentation

Random Numbers from Congruential Generator RANDU


400 triples of successive random numbers were taken from the VAX FORTRAN function RANDU running under VMS 1.5.




A data frame with 400 observations on 3 variables named x, y and z which give the first, second and third random number in the triple.


In three dimensional displays it is evident that the triples fall on 15 parallel planes in 3-space. This can be shown theoretically to be true for all triples from the RANDU generator.

These particular 400 triples start 5 apart in the sequence, that is they are ((U[5i+1], U[5i+2], U[5i+3]), i= 0, ..., 399), and they are rounded to 6 decimal places.

Under VMS versions 2.0 and higher, this problem has been fixed.


David Donoho


## We could re-generate the dataset by the following R code
seed <- as.double(1)
RANDU <- function() {
    seed <<- ((2^16 + 3) * seed) %% (2^31)
for(i in 1:400) {
    U <- c(RANDU(), RANDU(), RANDU(), RANDU(), RANDU())
    print(round(U[1:3], 6))