starting with 0,1,2... (!) Just pick one :-)"
So, there will be so many "possible" answers but
"unacceptable". (Actually, not as many as 5358,
because the search engine includes "0, 1, -2, ...";
"0, -1, 2, ..."; and "0, -1, -2, ..." as well as
"0, 1, 2, ...".)
As I said in a reply to Steve/Horst, there are an infinite number of series that can be shown mathematically to derive from "0, 1, 2,..." or indeed any starting sequence. The desire is for the most elegant (some of which I have excluded by clarifying my position, I know - I still really like "...10, 11, 12, 20,...").
following sequence has any use or ever found by
others:
n^(n!-floor(n/2)); n = 0, 1, 2, ...
You'll get the series: 0, 1, 2, 243, 1.75922E+13,
3.00927E+82, ...
To avoid too many possible answers, we may ask for
the largest fourth term. The winner is the one who
gets the largest fourth term.