On Sunday 18 May 2008 02:49:25 pm paul at clubi.ie wrote:
> I was simply pointing out that f(n) mod m is not necessarily (or
> > even usually) periodic, as someone had suggested.
>> I probably fail for relying on Wikipedia and Google, but which f(n)'s
> do you have in mind?
If f:N->N is a function then f(n) mod n is not necessarily
(or even usually) periodic.
I already gave examples of such functions,
namely the nth digit of pi or e (or sqrt2).
Or the continued fraction for the cube root of 2.
Etc, etc.
As I said, almost any sequence you think of
is going to be non-periodic,
unless there is some simple reason why it is periodic,
eg the decimal expansion of a rational number like 1/7 .
Nb I am not recommending any of these for pseudo-random number generation.
--
Timothy Murphy
e-mail: gayleard /at/ eircom.net
tel: +353-86-2336090, +353-1-2842366
s-mail: School of Mathematics, Trinity College, Dublin 2, Ireland
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