A049998

[Robert G. Wilson v]

Dear Berny,

	Using the code written in Mathematica below, I computed the first 2250
rows and then tested to see if any were not members of the Fibonacci sequence.
I found none.

Sincerely yours, Bob.


n=2250;
t = Take[ Union[ Flatten[ Table[ Fibonacci[i]Fibonacci[j], {i, 0, n}, {j, 0, i}]]], Floor[n(n + 1)/4]];
u = Union[Drop[t, 1] - Drop[t, -1]];
v = Table[Fibonacci[i], {i, n}];
Select[u, FreeQ[v, #] &]



Berny wrote:

> David Wilson says:
> 
>> Is A049998 composed entirely of Fibonacci numbers?
> 
> 
> Rearranging A049998:
> 
> 1
> 1
> 1   1
> 1   1
> 2   1   1
> 3   2   1
> 5   3   1  1
> 8   5   1  2
> 13  8   1  1 3
> 21  13  2  1 5
> 34  21  3  1 1 8
> 55  34  5  1 2 13
> 89  55  8  1 1 3  21
> 144 89  13 2 1 5  34
> 233 144 21 3 1 1  8  55
> 
> Someone willing to find a proof?
> 
>                Berny Boncompagni
> 
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