I haven't looked at "Farey-depth". Maybe someone on this list could work out the initial terms of the two sequences in 2.?
Earliest occurrences of odd denominators 3,5,7,...,201: 1,2,2,2,3,3,4,3,3,4,4,4,3,4,4,5,5,5,5,4,4,5,4,5,6, 4,4,6,5,6,5,5,5,5,5,5,5,5,5,4,5,6,7,6,6,6,6,6,5,6, 5,6,6,6,6,5,6,7,6,6,6,6,6,6,6,5,6,5,7,7,6,6,7,7,6, 7,6,6,6,5,5,7,6,6,6,7,7,7,6,6,6,7,7,6,7,7,7,6,7,7 Latest occurrences of odd denominators 3,5,7,...,29: 1,3,3,4,5,6,7,8,9,10,11,12,13,14,15 (The glitch in the second term of the second of these sequences reflects the fact that 2/5 and 3/5 don't show up until the 3rd iteration; whereas for n>2, it appears that the last fraction with denominator 2n+1 to show up is 1/(2n+1), and that this fraction shows up after exactly n iterations.) Here's the Mathematica code I used: Denom[L_, k_] := Module[{M, i}, M = {}; For[i = 1, i <= Length[L], i++, If[Denominator[L[[i]]] == k, M = Append[M, L[[i]]]]]; Return[M]] Earliest[k_] := Module[{i}, For[i = 1, Length[Denom[WF[i], k]] == 0, i++]; Return[i]] Latest[k_] := Module[{i}, For[i = 1, Length[Denom[WF[i], k]] < EulerPhi[k], i++]; Return[i]] Table[Earliest[2 n + 1], {n, 1, 100}] Jim