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A096552 Consecutive internal states of the linear congruential pseudo-random number generator MTH$RANDOM that is used in the VAX VMS Library.

%I A096552 #20 Jun 23 2025 19:37:43
%S A096552 0,1,69070,475628535,3277404108,772999773,3877832058,3821835443,
%T A096552 1662200408,2044158073,3788989926,797919023,2743624612,1156259413,
%U A096552 1059494674,584849259,786050992,3369345009,3077427454,1200308583,2654771836,1692139853,4052415402,1850655011
%N A096552 Consecutive internal states of the linear congruential pseudo-random number generator MTH$RANDOM that is used in the VAX VMS Library.
%C A096552 This generator is a variant of A096551.
%H A096552 Alois P. Heinz, <a href="/A096552/b096552.txt">Table of n, a(n) for n = 1..10000</a>
%H A096552 George S. Fishman, <a href="https://doi.org/10.2307/2008698">Multiplicative Congruential Random Number Generators with Modulus 2^beta: An Exhaustive Analysis for beta = 32 and a Partial Analysis for beta = 48</a>, Math. Comp., 54, 189 (1990), 331-344.
%H A096552 B. D. Ripley, <a href="https://doi.org/10.2307/1402590">Computer Generation of Random Variables: A Tutorial</a>, International Statistical Review, 51 (1983), 301-309.
%H A096552 B. D. Ripley, <a href="https://doi.org/10.1016/0377-0427(90)90346-2">Thoughts on pseudorandom number generators</a>, J of Computational and Applied Mathematics, 31, 1 (1990), 153-163.
%H A096552 <a href="/index/Ps#PRN">Index entries for sequences related to pseudo-random numbers.</a>
%F A096552 a(1)=0, a(n) = (69069*a(n-1)+1) mod 2^32. The sequence is periodic with period length 2^32. [Corrected based on a comment from _Kevin Ryde_, Nov 13 2024]
%p A096552 a:= proc(n) option remember; `if`(n<2, 0,
%p A096552       irem(69069 *a(n-1)+1, 4294967296))
%p A096552     end:
%p A096552 seq(a(n), n=1..30);  # _Alois P. Heinz_, Jun 10 2014
%t A096552 NestList[Mod[#*69069 + 1, 2^32] &, 0, 50] (* _Paolo Xausa_, Aug 29 2024 *)
%Y A096552 Cf. A096550-A096561 for other pseudo-random number generators.
%K A096552 nonn
%O A096552 1,3
%A A096552 _Hugo Pfoertner_, Jul 18 2004