30
7.9
Let us start with an initial seed of 1. The first generator yields the sequence:
1, 6, 10, 8, 9, 2, 12, 7, 3, 5, 4, 11, 1, . . .
The second generator yields the sequence:
1, 7, 10, 5, 9, 11, 12, 6, 3, 8, 4, 2, 1, . . .
Because of the patterns evident in the second half of the latter sequence, most
people would consider it to be less random than the first sequence.
7.10
When
m
= 2
k
, the righthand digits of
X
n
are much less random than the lefthand
digits. See [KNUT98], page 13 for a discussion.
7.11
Many packages make use of a linear congruential generator with
m
= 2
k
. As
discussed in the answer to Problem 10, this leads to results in which the righthand
digits are much less random than the lefthand digits. Now, if we use a linear
congruential generator of the following form:
X
n
+1
= (a
X
n
+ c) mod
m
then it is easy to see that the scheme will generate all even integers, all odd integers,
or will alternate between even and odd integers, depending on the choice for a and
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 Fall '11
 Dr.TimothyCerner
 Natural number, Greatest common divisor, Pseudorandom number generator, odd integers, SIGCSE Bulletin, Cesaro

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