[seqfan] Re: A033473

israel at math.ubc.ca israel at math.ubc.ca
Mon Feb 17 08:09:45 CET 2014


One problem with "Nearest integer to ..." is that many of the denominators 
that are not 1 are 2, and "nearest" leaves ambiguous whether you round up 
or down.

Robert

On Feb 16 2014, M. F. Hasler wrote:

>On Sun, Feb 16, 2014 at 8:38 PM,  <franktaw at netscape.net> wrote:
>> I would definitely favor "Numerator of", and add the denominator 
>> sequence, too. Exact fractional values are much more interesting than 
>> rounded values.
>
>I agree upon that in general, but here the sequence was defined
>precisely in the goal of converting a sequence of fractions to an
>integer sequence (e.g. to study growth of the ("original") sequence
>(of fractions), or the like).
>It makes no sense to multiply by 8 if one wants (exact) fractions; the
>latter are maybe there or else should be added as new sequences (for
>the original sequence of fractions, maybe multiplied by the
>factorial).
>IMHO it would be quite unnatural to have a sequence of "numerators"
>for which most denominators are equal to 1 (because all were supposed
>to be so).
>
>Maximilian
>
>> -----Original Message-----
>> From: M. F. Hasler <seqfan at hasler.fr>
>> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>> Sent: Sun, Feb 16, 2014 6:28 pm
>> Subject: [seqfan] Re: A033473
>>
>>
>> On Sun, Feb 16, 2014 at 6:40 PM, <israel at math.ubc.ca> wrote:
>>
>>> According to Maple, A033473 is not an integer sequence: the first few
>>> non-integer terms given by the formula (2*n+1)!*8*bernoulli(2*n,1/2)
>>
>> are
>>>
>>> for n = 15, 23, 27, 29, 30, 31, 39, 43, 45, 46, 47, the corresponding
>>> denominators being 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 4.
>>>
>>
>>
>> PARI (& me) agree.
>>
>> I propose to change the name to "Nearest integer to ..."
>> But "Floor ..." or "Numerator of ..." would also leave the integer terms
>> invariant.
>>
>> Maximilian
>>
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