

A096555


Consecutive internal states of the linear congruential pseudorandom number generator RANDU that was used in the IBM Scientific Subroutine Library for IBM System/360 computers in the 1970's.


1



1, 65539, 393225, 1769499, 7077969, 26542323, 95552217, 334432395, 1146624417, 1722371299, 14608041, 1766175739, 1875647473, 1800754131, 366148473, 1022489195, 692115265, 1392739779, 2127401289, 229749723, 1559239569
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OFFSET

1,2


COMMENTS

Due to a poor choice of the multiplier the generator fails most 3d criteria for randomness. 9*a(n2)6*a(n1)+a(n) = 0 mod 2^31. This was first described by George Marsaglia. The Java applet given in the link demonstrates the deficient behavior.


REFERENCES

D. E. Knuth, The Art of Computer Programming Third Edition. Vol. 2 Seminumerical Algorithms. Chapter 3.3.4 The Spectral Test, Page 107. AddisonWesley 1997.
Marsaglia G., Random numbers fall mainly in the planes, Proceedings of the National Academy of Sciences, 61, 2528, 1968


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Sarah Belet, 'Round the Twist, Blog Entry, Friday May 16 2014
Java applet demonstrating random number generation with the Linear Congruential Method.
Index entries for sequences related to pseudorandom numbers.


FORMULA

a(1)=1, a(n) = 65539*a(n1) mod 2^31. The sequence is periodic with period length 2^29.


MAPLE

a:= proc(n) option remember; `if`(n<2, n,
irem(65539 *a(n1), 2147483648))
end:
seq(a(n), n=1..30); # Alois P. Heinz, Jun 10 2014


PROG

(PARI) a(n)=lift(Mod(65539, 2^31)^(n1)) \\ Charles R Greathouse IV, Jan 13 2016


CROSSREFS

Cf. A096550A096561 for other pseudorandom number generators.
Sequence in context: A133865 A194185 A282777 * A258533 A258526 A254918
Adjacent sequences: A096552 A096553 A096554 * A096556 A096557 A096558


KEYWORD

nonn,easy


AUTHOR

Hugo Pfoertner, Jul 19 2004


STATUS

approved



