A049998

[Dean Hickerson]

David Wilson wrote:

> I will go out on a limb and conjecture that the difference between two
> adjacent numbers that are the product of n Fibs is the product of n-1 Fibs.
> I have little evidence, it just seems like it would be a nice thing to be
> true.

It's false for n=3:  There are no products of 3 Fibs between 110 = 1*2*55
and 117 = 3*3*13, but 117-110 = 7 is not a product of any number of Fibs.

Looking at products of 3 Fibs up to Fib(200), the first few numbers that don't
occur as differences (of consecutive products) are 12, 17, 19, 20, 22, 27,
28, 30.  I don't know if these occur if we use larger Fibs.

Dean Hickerson
dean at math.ucdavis.edu