[seqfan] Re: A098550

Benoît Jubin benoit.jubin at gmail.com
Wed Nov 26 18:39:47 CET 2014


Dear Frank and seqfans,

This is interesting (that A098550(n)/n has a discrete set of adherence
values). Do you have approximate values for the first few?
Have you looked at the probably simpler sequence A098548?
For it, one can prove that:
a(n) is even if and only if n is even
a(2n) = a(2n-1)+1
a(2n+1)-a(2n) is at least 5
and in particular a(n)>3n for n large enough, but I cannot prove that
a(n)<Kn for some K. Empirically, a(2n+1) seems to be a multiple of 3
and a(2n+1)-a(2n) seems to be prime (5,11,17...) and a(n)/n seems to
have a limit close to 4.

I think it would be worth adding the squarefree parts of A098548 and A098550.

Benoît

On Fri, Nov 21, 2014 at 6:07 PM, Frank Adams-Watters
<franktaw at netscape.net> wrote:
> This sequence has what at first seems to be at most a marginally interesting
> graph: several straight lines. But when we look at a(n)/n:
>
> https://oeis.org/plot2a?name1=A098550&name2=A000027&tform1=untransformed&tform2=untransformed&shift=0&radiop1=ratio&drawpoints=true
>
> it gets more interesting. The lines do not have integral slope, as one would
> expect them to have. Any insights into what what is going on here?
>
> Franklin T. Adams-Watters
>
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>
> Seqfan Mailing list - http://list.seqfan.eu/


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