# [seqfan] Re: Near-linear sequence

Aai agroeneveld400 at gmail.com
Mon Sep 1 08:30:36 CEST 2014

```Thanks Neil. That's what I meant. Sorry for the typo and confusing.

On 31-08-14 21:01, Neil Sloane wrote:
> 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/
>
>

--
Met vriendelijke groet,
@@i = Arie Groeneveld

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