(Almost)Consecutive-Integer Egyptian-Fraction Sum =1
Leroy Quet
qq-quet at mindspring.com
Mon May 24 17:02:59 CEST 2004
[posted also to sci.math.]
I was led to this question by considering (m+1)-sided polygons where all
but one of the sides are that of a k-gon, a (k+1)-gon, a (k+2)-gon,...,
an (k+m)-gon.
But I wanted the final angle to be that of an n-gon, for some positive
integer n.
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?
thanks,
Leroy Quet
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