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Whole Number Dynamics I

The first of five articles concentrating on whole number dynamics, ideas of general dynamical systems are introduced and seen in concrete cases.

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Whole Number Dynamics II

This article extends the discussions in "Whole number dynamics I". Continuing the proof that, for all starting points, the Happy Number sequence goes into a loop or homes in on a fixed point.

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Whole Number Dynamics III

In this third of five articles we prove that whatever whole number we start with for the Happy Number sequence we will always end up with some set of numbers being repeated over and over again.

Difference Dynamics

Age 14 to 18 Challenge Level:

This iterative process produces a chain of different sequences which is actually a sequence of sequences . Start with short sequences of small numbers so that you can easily produce a chain of sequences and notice patterns. Look out for sequences that have already occured earlier in your chain.