[seqfan] Re: Near-linear sequence

[Aai]

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
>>
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>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>

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Met vriendelijke groet,
@@i = Arie Groeneveld