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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



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