20021024, 21:51  #1 
2^{2}×2,399 Posts 
Fibonacci sums?
Is 2^p 1 always the sum of p Fibonacci numbers?
examples: 3=1+2 7=1+1+5 31=2+3+5+8+13 127=1+1+2+13+21+34+55 2047= ...............................? 8191=1+1+5+21+34+55+89+233+377+610+987+1597+4181 I cant seem to find the sum for p=11. 
20021025, 03:27  #2  
Aug 2002
110100_{2} Posts 
Re: Fibonacci sums?
Quote:
Quote:
There are more. 

20021025, 21:47  #3  
Aug 2002
Portland, OR USA
2×137 Posts 
Re: Fibonacci sums?
Quote:
Is 2^p  1 always the sum of p Unique* Fibonacci numbers? *(unique as in use each number once) The smaller p will be difficult: 7 = 1+1+5 = 2+2+3 ... I see no solution for 3. To prove or disprove either of these questions, it is sufficient to find the fewest q < p Fibonacci numbers needed to sum each Mp. i.e. if you can always express Mp as the sum of 5 Fn, then you can replace F(n) with F(n1) + F(n2), then repeat the process until you have p numbers. 

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