20150917, 18:07  #56 
Jul 2014
702_{8} Posts 
The final page as promised.
http://www.mersenneforum.org/attachm...1&d=1442513118 That's the proof. The rest of it shows that all series of reciprocals of a set of postive integers which has no a.p's more than 2 long is bounded above by 6. According to my reasoning that settles the case for 3 mentioned as being open on the wikipedia. /* EDIT : I aught to say : this is because this sequence with no a.p's more than 2 long, is the sequence whose associated series of reciprocals is bounded above by 6 and all other sequences with no a.p's more than 2, have a series of reciprocals for which each term is dominated by the corresponding term of the former. */ Last fiddled with by wildrabbitt on 20150917 at 18:16 
20150917, 18:19  #57  
"Forget I exist"
Jul 2009
Dartmouth NS
20E2_{16} Posts 
Quote:


20150917, 18:26  #58 
Jul 2014
702_{8} Posts 
Thanks for letting know. It's quite condensed maths but it's not too hard. I don't blame you though for not going to pains to
check it. 
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