[seqfan] Re: Near-linear sequence

[Neil Sloane]

Arie said:

It looks like that the list of partial sums of A164349is equal toA10140.

but more to the point, what he meant was:

It looks like that the list of partial sums of A164349 is equal to A101402,

a very nice remark, since the latter is the sequence this discussion
is all about.

But the discussion has gone off the boil - nothing for three days.
Benoit, can you wrap it up before the semester begins
 in a few days?

Neil

Neil

On Thu, Aug 28, 2014 at 4:23 AM, Aai <agroeneveld400 at gmail.com> wrote:
> Sorry. Premature sending.
>
>
>
> It looks like that the list of partial sums of A164349is equal toA10140.
>
> A164349 comment
>
> The proportion of 0's in this sequence converges to a number close to
> 0.645059.The constantsuggested by you is also
>
> 1 - 0.645059 = 0.354941
>
> the proportion of the number of 1's.
>
>
>
>
>
>
>
>> On 27-08-14 18:39, Charles Greathouse wrote:
>>>
>>> Sequence A101402 appears to be nearly linear. For the first 10,000 terms
>>> there is a constant k such that |a(n) - kn| < 2 (e.g., take k = 0.355).
>>> Can
>>> anyone prove or disprove that a(n) = kn + O(1) for some constant k? In
>>> the
>>> (likely?) latter case, can another reasonable bound be found, maybe O(log
>>> n)? I can't even think of a technique that would work here.
>>>
>>> I just checked to a million and it looks like the same holds. Here I used
>>> k
>>> = 0.3549419505. Probably going to 10 million would require relaxing the
>>> bound slightly; already by a million the choice of constant is very
>>> constrained.
>>>
>>> Charles Greathouse
>>> Analyst/Programmer
>>> Case Western Reserve University
>>>
>>> _______________________________________________
>>>
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
>
> --
> Met vriendelijke groet,
> @@i = Arie Groeneveld
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/



-- 
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
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