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James Tanton
"Bumped Fibonacci": 0,1,2,4,7,12,20,33,... Each nmbr is one more than sum of previous two. What's the 100th nmber in this list?
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Varun Goel 5 Apr 13
Replying to @jamestanton
If BF(n) is the nth Bumped fibonacci number and F(n) the nth fibonacci number, then: BF(n)=BF(n-1)+F(n)
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James Tanton 5 Apr 13
Replying to @varungoel431
Yes! AND ... also try adding 1 to each of the BF(n) numbers!
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Varun Goel 5 Apr 13
Replying to @jamestanton
Yes, adding one will result in the normal Fibonacci series !!
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James Tanton 5 Apr 13
Replying to @varungoel431
Do you see why?
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Varun Goel 5 Apr 13
Replying to @jamestanton
Not exactly, why??
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Varun Goel 5 Apr 13
Replying to @jamestanton
Another interesting observation:
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James Tanton 5 Apr 13
Replying to @varungoel431
BF(n+2) =BF(n+1) + BF(n) + 1. So.. [BF(n+2)+1] = [BF(n+1)+1] + [BF(n)+1] showing that BF(N)+1 is just the Fib sequence! Weird!
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