Another optimisation possible if N is odd, is to step back by 2 each time.
And if N is even, factor out all the powers of 2, and run the algorithm against the remaining factor. For example, 
1000 == 2**3 * 5**3

[download]
which leaves 
125 == 5**3

[download]
leading to 
5 * 2**2 == 20

[download]
as "close enough".

-QM
--
Quantum Mechanics: The dreams stuff is made of

In reply to Re^4: OT: Finding Factor Closest To Square Root by QM
in thread OT: Finding Factor Closest To Square Root by QM

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