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

Zak Seidov zakseidov at mail.ru
Mon Feb 8 06:20:57 CET 2016




>Понедельник,  8 февраля 2016, 8:07 +03:00 от Zak Seidov <zakseidov at mail.ru>:
>
>sorry A268515 (19)=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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