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%I #18 Oct 19 2022 21:09:48
%S 1,65539,393225,1769499,7077969,26542323,95552217,334432395,
%T 1146624417,1722371299,14608041,1766175739,1875647473,1800754131,
%U 366148473,1022489195,692115265,1392739779,2127401289,229749723,1559239569
%N 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.
%C 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.
%D 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.
%D Marsaglia G., Random numbers fall mainly in the planes, Proceedings of the National Academy of Sciences, 61, 25-28, 1968
%H Alois P. Heinz, <a href="/A096555/b096555.txt">Table of n, a(n) for n = 1..10000</a>
%H Sarah Belet, <a href="http://www.aums.org.au/talks/s_belet/SarahB_Round_the_Twist.pdf">'Round the Twist</a>, Blog Entry, Friday May 16 2014 [broken link]
%H <a href="http://www.cs.pitt.edu/~kirk/cs1501/animations/Random.html">Java applet demonstrating random number generation with the Linear Congruential Method.</a>
%H <a href="/index/Ps#PRN">Index entries for sequences related to pseudo-random numbers.</a>
%F a(1)=1, a(n) = 65539*a(n-1) mod 2^31. The sequence is periodic with period length 2^29.
%p a:= proc(n) option remember; `if`(n<2, n,
%p irem(65539 *a(n-1), 2147483648))
%p end:
%p seq(a(n), n=1..30); # _Alois P. Heinz_, Jun 10 2014
%o (PARI) a(n)=lift(Mod(65539,2^31)^(n-1)) \\ _Charles R Greathouse IV_, Jan 13 2016
%Y Cf. A096550-A096561 for other pseudo-random number generators.
%K nonn,easy
%O 1,2
%A _Hugo Pfoertner_, Jul 19 2004
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