[seqfan] Egyptian Fractions and pi

Victor Miller victorsmiller at gmail.com
Mon Mar 17 22:17:37 CET 2014


I was fiddling with the greedy algorithm for representing a positive
rational as an Egyptian Fraction (a sum of fractions of the form 1/m) and I
applied it to some of the convergents of pi, and noticed that denominators
in the Egyptian fraction started to stabilize.  A little thought shows that
the greedy algorithm can be applied to any positive real (of course, if
it's not rational, it will be an infinite sequence).  I found the sequence
starting with

1,2,3,4,5,6,7,8,9,10,11,12,27,744,1173268,
2586625801171,14348276635209672362238685,...

which is not in OEIS.  It's amusing the way that it starts.


Victor



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