Re: Find (cyclic) Sequence
- To: mathgroup at smc.vnet.net
- Subject: [mg109348] Re: Find (cyclic) Sequence
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Fri, 23 Apr 2010 03:47:01 -0400 (EDT)
You are looking for a solution of the form
f[a_, b_] = Mod[a + b*#, 4] &;
seqIn = {0, 3, 2, 1};
seqOut = {0, 1, 2, 3};
sol =
Reduce[
Thread[
f[a, b] /@ seqIn == seqOut],
{a, b}, Integers]
Element[C[1] | C[2], Integers] &&
a == 4*C[1] && b == 4*C[2] + 3
Picking values for the arbitrary constants
sol /. {C[1] -> 1, C[2] -> -1}
a == 4 && b == -1
Verifying
f[4, -1] /@ seqIn == seqOut
True
Bob Hanlon
---- mokambo <alexandrepassosalmeida at gmail.com> wrote:
=============
Dear Group:
Consider the following sequence {0,3,2,1} which can be related to the
reference k: {0,1,2,3} as 4-k (mod 4).
I've tried to use FindSequenceFunction on problems like the example
above without success.
I understand I'm working within the context of modular arithmetic...
Does anyone have a suggestion on how to use Mathematica to tackle this
problem?
Alex