[seqfan] Re: A033473

M. F. Hasler oeis at hasler.fr
Mon Feb 17 06:48:46 CET 2014


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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