[seqfan] Re: is continued fraction expansion of 2^(1/3) bounded?

Zak Seidov zakseidov at mail.ru
Mon Feb 8 06:07:58 CET 2016


 A181495(18)=13761184

From first 20000000 terms of A002945:
A002945(12918396)=13761184
as Bob 'd found.
>Воскресенье,  7 февраля 2016, 22:41 -05:00 от Neil Sloane <njasloane at gmail.com>:
>
>Robert, Thanks for that important comment, which explains a great deal. I
>have taken the liberty of adding a version of the comment to A181495.
>
>Best regards
>Neil
>
>Neil J. A. Sloane, President, OEIS Foundation.
>11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
>Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
>Phone: 732 828 6098; home page:  http://NeilSloane.com
>Email:  njasloane at gmail.com
>
>
>On Sun, Feb 7, 2016 at 10:08 PM, < israel at math.ubc.ca > wrote:
>
>> The 19 terms currently present in A181495 require computing at least
>> 12918396 terms of the continued fraction of 2^(1/3). I don't know how many
>> more were computed without finding another term, but the given Mma code
>> computes 20000000. I think that's numerically very demanding, requiring
>> terrifically high precision. Maybe somebody can grind out a few more terms,
>> but I doubt we'll get enough to require a b-file.
>>
>> Cheers,
>> Robert
>>
>> On Feb 7 2016, Neil Sloane wrote:
>>
>> It seems that this is an open problem.  See A002945, A181495, A268515.  The
>>> last two need more terms, or even better, b-files
>>> .
>>> Best regards
>>> Neil
>>>
>>> Neil J. A. Sloane, President, OEIS Foundation.
>>> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
>>> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
>>> Phone: 732 828 6098; home page:  http://NeilSloane.com
>>> Email:  njasloane at gmail.com
>>>
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