|
| |
|
|
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.
|
|
0
| |
|
|
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; 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
| Java applet demonstrating random number generation with the Linear Congruential Method.
|
|
|
FORMULA
| a(1)=1, a(n) = 65539*a(n-1) mod 2^31. The sequence is periodic with period length 2^29.
|
|
|
CROSSREFS
| Cf. A096550 - A096561 for other pseudo-random number generators.
Sequence in context: A036094 A133865 A194185 * A168667 A170781 A063825
Adjacent sequences: A096552 A096553 A096554 * A096556 A096557 A096558
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Hugo Pfoertner (hugo(AT)pfoertner.org), Jul 19 2004
|
| |
|
|
