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A096555 Consecutive internal states of the linear congruential pseudo-random 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Due to a poor choice of the multiplier the generator fails most 3-d criteria for randomness. 9*a(n-2)-6*a(n-1)+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. Addison-Wesley 1997.

Marsaglia G., Random numbers fall mainly in the planes, Proceedings of the National Academy of Sciences, 61, 25-28, 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 pseudo-random numbers.

FORMULA

a(1)=1, a(n) = 65539*a(n-1) 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(n-1), 2147483648))

    end:

seq(a(n), n=1..30);  # Alois P. Heinz, Jun 10 2014

PROG

(PARI) a(n)=lift(Mod(65539, 2^31)^(n-1)) \\ Charles R Greathouse IV, Jan 13 2016

CROSSREFS

Cf. A096550-A096561 for other pseudo-random 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

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Last modified October 21 00:56 EDT 2017. Contains 293679 sequences.