About egyptian fractions (from POWT-L)
David Broadhurst
D.Broadhurst at open.ac.uk
Tue Mar 24 01:43:23 CET 1998
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
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Dr D J Broadhurst Email: D.Broadhurst at open.ac.uk
Reader in Physics Phone: (+44) 1908 655132 (Yvonne Mckay)
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