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 2015-09-17, 18:07 #56 wildrabbitt   Jul 2014 7028 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. */ Attached Thumbnails   Last fiddled with by wildrabbitt on 2015-09-17 at 18:16
2015-09-17, 18:19   #57
science_man_88

"Forget I exist"
Jul 2009
Dartmouth NS

20E216 Posts

Quote:
 Originally Posted by wildrabbitt 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. */
I'm not responding mostly because I just suck at math in general.

 2015-09-17, 18:26 #58 wildrabbitt   Jul 2014 7028 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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