[seqfan] Re: How to calculate oblong root?

[Neil Sloane]

> The floor is not in the database.
Please add it!
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 Mon, Jun 22, 2015 at 12:24 AM, Frank Adams-Watters
<franktaw at netscape.net> wrote:
> Note that the ceiling of this function (sqrt(n+1/4)-1/2) is A000194. The floor is not in the database.
>
> Franklin T. Adams-Watters
>
> -----Original Message-----
> From: David Applegate <david at research.att.com>
> To: seqfan <seqfan at list.seqfan.eu>
> Sent: Sun, Jun 21, 2015 10:57 pm
> Subject: [seqfan] Re: How to calculate oblong root?
>
>
> That definition of oblongroot(n) is ambiguous.  If n is not an oblong
> number,
> then any x that satisfies
> floor(oblongroot(n)) < x < ceil(oblongroot(n))
> will
> also satisfy the definition of oblongroot(n).
>
> Why not just define
> oblongroot(n)=m, where m satisfies m^2 + m = n,
> that is, oblongroot(n) =
> sqrt(n+1/4)-1/2 (and the secondary oblong
> root is -sqrt(n+1/4)-1/2)?
>
> David
> Applegate               AT&T Labs Research
> Tel:    +1 908 901 2004       Email:
> david at research.att.com
>                               Recycle yourself -- be an
> organ donor
>
>> From seqfan-bounces at list.seqfan.eu Sun Jun 21 21:48:44 2015
>>
> Date: Sun, 21 Jun 2015 21:47:43 -0400
>> From: Alonso Del Arte
> <alonso.delarte at gmail.com>
>> To: Sequence Fanatics Discussion list
> <seqfan at list.seqfan.eu>
>> Subject: [seqfan] How to calculate oblong root?
>
>> The
> principal square root function is a function that is useful not only in
>>
> mathematics but in many sciences. The principal oblong root function is
>>
> significantly less useful, but once in a while it comes in handy, as in for
>>
> example, the oblong number equivalent of A048761, the smallest square
>> greater
> than or equal to n.
>
>> If n is an integer of the form m * (m + 1) or m^2 + m
> with m also an
>> integer, then oblongroot(n) = m. But if n is not of that form,
> then
>> oblongroot(n) returns some number, possibly irrational, such that
>>
> floor(oblongroot(n)) * ceiling(oblongroot(n)) is the smallest oblong number
>>
> greater than n.
>
>> Maybe the formula for oblongroot(n) is very easy, but at the
> moment, I
>> don't see what it is.
>
>> Al
>
>> P.S. The secondary oblong root is a
> negative integer of the form -(m + 1),
>> e.g., -5 is the secondary oblong root
> for 20.
>
>> --
>> Alonso del Arte
>> Author at SmashWords.com
>>
> <https://www.smashwords.com/profile/view/AlonsoDelarte>
>> Musician at
> ReverbNation.com <http://www.reverbnation.com/alonsodelarte>
>
>>
> _______________________________________________
>
>> Seqfan Mailing list -
> http://list.seqfan.eu/
>
>
> _______________________________________________
>
> Seqfan
> Mailing list - http://list.seqfan.eu/
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/