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

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 [broken link]

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 * A362950 A258533 A258526

Adjacent sequences: A096552 A096553 A096554 * A096556 A096557 A096558

Keyword

nonn,easy

Author

Hugo Pfoertner, Jul 19 2004

Status

approved