probabilistic number theory

[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. */

[science_man_88]

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.

[wildrabbitt]

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.