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Is there a way to determine a pattern in a sequence which elements are known to be the result of a modulus operation ?

Say I have 0,1,2,0,1,2,0. It is $\{i mod 3\}$ for $i$ going from $0$ to $6$

That is what I mean by modulus (modulo?) operation,

Or is it by trial and error most likely ?

Cheers.

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    For example, see: http://oeis.org/A204425 Such sequences could arise from many things and without knowing more numbers it could be anything.2012-12-08

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Say I have 0,1,2,0,1,2,0.

This is i(i+1)(i+4)(6i3+6i2+3i+4) mod 7 for i going from i = 0 to i = 6 hence the next term of the sequence is 0 (in case you would have the idea that the next term should be, say... 1).