[seqfan] How to calculate oblong root?

[Alonso Del Arte]

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.

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Alonso del Arte
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