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Strange sequence (Posted on 2005-11-15) Difficulty: 4 of 5
If f(0)=0 and for n>0, f(n)=n-f(f(n-1)),
what is f(1,000,000,000,000)?

Computer solutions welcome,
though a proof would be better!

See The Solution Submitted by e.g.    
Rating: 3.1667 (6 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: solution - no computer | Comment 3 of 9 |
(In reply to solution - no computer by pcbouhid)

Well done!

Out of curiosity, is there an implied assumption or is it just obvious.  The behavior in the limit does not necessarily apply across the range of the function.  It works in this case because the function is a linear function of a linear function and therefore is linear overall.  True?


  Posted by Bob Smith on 2005-11-15 14:15:57
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