

A177903


Consider the weighted Farey tree A177405/A177407; a(n) = row at which the denominator 2n+1 first appears (assumes first row is labeled row 0).


4



0, 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
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OFFSET

0,3


COMMENTS

Latest occurrences of odd denominators 1,3,5,7,...,29: 0,1,3,3,4,5,6,7,8,9,10,11,12,13,14,15 (The glitch in the third term 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.)  James Propp


REFERENCES

Based on postings by Richard C. Schroeppel and James Propp to the Math Fun Mailing List, Dec 15 2010.


LINKS

Table of n, a(n) for n=0..100.


MATHEMATICA

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}]
(* James Propp *)


CROSSREFS

Cf. A177405, A177407. See A178042 for another version. Cf. also A178031.
Sequence in context: A038809 A337496 A078342 * A107325 A003050 A070868
Adjacent sequences: A177900 A177901 A177902 * A177904 A177905 A177906


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Dec 15 2010


STATUS

approved



