Hello Math-Fun, Fractions have always fascinated me and I was recently wondering: what about a finite subset of them, whose elements might be counted? So I started with this: « Fractions having no duplicate digit », with the examples 123/456, or 20983/1 -- but not 10657/2314 because of the duplicated "1". Two questions: a) how many such "no-dup fractions" are there in the subset? b) how could one start a seq for the OEIS with those? Question (a) is far too complicated for me because of the huge amount of such "no-dup fractions"; Question (b): Suppose we have them all, how could we now sort the "no-dup frations" from the smallest one (I guess the smallest one is 1/987654320) to the biggest one (I guess 987654320/1)? This problem arises when we bump into frations which are no-dup BUT equivalent: 1/2, 134/268, 15/30, 78/156,... In such a subset of "equivalent no-dup fractions" there is no smallest or biggest fraction, there is no order, they are all "the same". Except if we decide to take into account (for this subset only) the numerators -- and to sort the said subset with them. We would then start for instance the subset of "equivalent to 1/2 no-dup fractions" with: 1/2, 2/4, 3/6, 4/8, 5/10, 6/12, 7/14, 8/16, 9/18, 13/26, 14/28, 15/30, 16/32, 17/34, 18/36, 19/38, 23/46, 26/52, etc. This rule allows us to sort all those no-dup fractions with this simple (?) method: - find all a/b no-dup fractions - compute all a/b to the 10th decimal and sort those computations - if two ore more a/b computations have the same result, sort according to "a" (smallest "a" first, then second "a", etc.) Now that we have a complete list of no-dup fractions starting with the smallest one and ending with the biggest one (with sorted "plateaus" all over), the final touch will consists in building a sound OEIS seq "S". I propose to use two successive terms of S to encode the fraction a/b with a(n) = "a" and a(n+1) = "-b". This minus sign before "b" solves it all (and reminds us that there is a fraction bar after a(n) separating the numerator "a" from the denominator |b| of the encoded no-dup fraction. Is this an interesting idea? At least, how many no-dup fractions are possible (in base 10)? Best, É.