About egyptian fractions (from POWT-L)

[David Broadhurst]

RE: Odd-greedy egyptian remainder-numerator sequences (see POWT-L #848)

David Bailey's fraction gives 27 terms:

 5/5809 ==>
 5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,
 1

Here are a pair with length=28:

 2/588391 ==>
 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,
 1

 4/538199 ==>
 4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,
 2,3,4,5,2,1

Here is one with length=29:

 3/46547 ==>
 3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,
 2,3,4,5,2,1

Finally, I found a pair with length=30:

 2/24631 ==>
 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,
 2,3,4,5,2,1

 6/104651 ==>
 6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,
 3,2,1

Question: Are sequences known with length > 30 ?

David Broadhurst
- ------------------------------------------------------------------------
Dr D J Broadhurst           Email: D.Broadhurst at open.ac.uk
Reader in Physics           Phone: (+44) 1908 655132 (Yvonne Mckay)
The Open University         FAX:   (+44) 1908 654192
Milton Keynes MK7 6AA, UK   http://physics.open.ac.uk/~dbroadhu/het.html