A096552 Consecutive internal states of the linear congruential pseudo-random number generator MTH$RANDOM that is used in the VAX VMS Library.
0, 1, 69070, 475628535, 3277404108, 772999773, 3877832058, 3821835443, 1662200408, 2044158073, 3788989926, 797919023, 2743624612, 1156259413, 1059494674, 584849259, 786050992, 3369345009, 3077427454, 1200308583, 2654771836, 1692139853, 4052415402, 1850655011
Offset: 1
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..10000
- George S. Fishman, Multiplicative Congruential Random Number Generators with Modulus 2^beta: An Exhaustive Analysis for beta = 32 and a Partial Analysis for beta = 48, Math. Comp., 54, 189 (1990), 331-344.
- B. D. Ripley, Computer Generation of Random Variables: A Tutorial, International Statistical Review, 51 (1983), 301-309.
- B. D. Ripley, Thoughts on pseudorandom number generators, J of Computational and Applied Mathematics, 31, 1 (1990), 153-163.
- Index entries for sequences related to pseudo-random numbers.
Programs
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Maple
a:= proc(n) option remember; `if`(n<2, 0, irem(69069 *a(n-1)+1, 4294967296)) end: seq(a(n), n=1..30); # Alois P. Heinz, Jun 10 2014 -
Mathematica
NestList[Mod[#*69069 + 1, 2^32] &, 0, 50] (* Paolo Xausa, Aug 29 2024 *)
Formula
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]
Comments