Re^3: Efficient enumeration of pandigital fractions

in reply to Re^2: Efficient enumeration of pandigital fractions
in thread Efficient enumeration of pandigital fractions

> doesn't mean that i < n/2, it's e

yeah I noticed. :)

> i can't be 1, base/2, base-2 and base-1

Why not base-2 ... could you elaborate?

8 * 12.. = 96.. base-10 ?

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Re^4: Efficient enumeration of pandigital fractions by kikuchiyo (Hermit) on Jul 22, 2018 at 06:20 UTC
Why not base-2 ... could you elaborate? 8 * 1234 (the smallest possible denominator) = 9872, which is just 4 away from the largest possible numerator, 9876, so there isn't much wiggle room there. But 8 is already taken, and the next possible combination 9765, is not divisible with 8, and the quotient is less than 1234. In general, `zyxw...(base/2-1) - (base-2) * 1234...(base/2-1) = base/2 - 1`.	[reply] [d/l]

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Re^4: Efficient enumeration of pandigital fractions
by kikuchiyo (Hermit) on Jul 22, 2018 at 06:20 UTC

Why not base-2 ... could you elaborate?

8 * 1234 (the smallest possible denominator) = 9872, which is just 4 away from the largest possible numerator, 9876, so there isn't much wiggle room there. But 8 is already taken, and the next possible combination 9765, is not divisible with 8, and the quotient is less than 1234.

In general, zyxw...(base/2-1) - (base-2) * 1234...(base/2-1) = base/2 - 1.

[reply]
[d/l]

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