If one indexes the sequence from t, then the function for each term is trivially
Because this is the end of the easy sequences, you get something a bit more tricky - another solution:
Part of what mathematicians do is look for patterns. But be warned, just because it *looks* like it's doing something doesn't mean it's going to keep doing it forever! Showing that something does actually follow a pattern is some of what mathematicians spend their time on. But don't worry about that now, go look at some more sequences!
A bit too trivial for my liking, what about
resulting in 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2...
What about any of these?
with k >= 4
The sequence wasn´t supposed to necessarily change from 1 to 2 exactly after the ellipsis ("...").
another solution: with
f(n) = f(n-1) ! for n > 1 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1...