[seqfan] Re: All integers a(n) > 20 are in sequence A246778

Charles Greathouse charles.greathouse at case.edu
Sun Nov 29 06:52:35 CET 2015


Yes, gaps should be less than x^0.75; in fact gaps are smaller than x^0.525
for large enough x. This is far larger than the Granville expected gap of
course.

As Vladimir mentioned we expect Firoozbakht's conjecture to be false
(though the first failure may be quite large -- IIRC the heuristic chance
of one up to 10^200 is only around 50%).

On Friday, November 27, 2015, Alexei Kourbatov <akourbatov at gmail.com> wrote:

> Dear Seqfans,
> Just added a new theorem in A246778 showing that all terms a(n)>20 are in
> the sequence (just as conjectured by Farideh Firoozbakht) - provided that
> prime gaps near x are less than x^0.75. Any feedback will be greatly
> appreciated. (If you happen to have a nicer/shorter proof, that would be
> great!)
> Alexei
>
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>


-- 
Charles Greathouse
Analyst/Programmer
Case Western Reserve University



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