(Almost)Consecutive-Integer Egyptian-Fraction Sum =1

[Ralf Stephan]

> For example,
> 
> 1/3 + 1/4 + 1/5 + 1/6 + 1/20 = 1.
> 
> So, my question is,
> 
> which integers n are such that:
> 
> 1/k + 1/(k+1) + 1/(k+2) +....+1/(k+m) + 1/n = 1 ?
> 
> What is the sequence of such n's? Is it in the EIS?

Sure there is more than your example plus 1/2+1/2 and 1/2+1/3+1/6?
For k up to 1000 my Kiste could find no more, and anyway, I feel
there is an easy proof but cannot substantiate it further.


ralf