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A174981 Numerators of the L-tree, left-to-right enumeration. 2
0, 1, 1, 2, 3, 1, 2, 3, 5, 2, 5, 3, 4, 1, 3, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 4, 5, 9, 4, 11, 7, 10, 3, 11, 8, 13, 5, 12, 7, 9, 2, 9, 7, 12, 5, 13, 8, 11, 3, 10, 7, 11, 4, 9, 5, 6, 1, 5, 6, 11, 5, 14, 9, 13, 4, 15, 11, 18, 7, 17, 10, 13, 3, 14, 11, 19, 8, 21, 13, 18, 5, 17, 12, 19, 7, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

a(n) is a subsequence of A174980. a(n)/A002487(n+2) enumerates all the reduced nonnegative rational numbers exactly once (L-tree).

LINKS

Table of n, a(n) for n=0..90.

Edsger Dijkstra, Selected Writings on Computing, Springer, 1982, p. 232. EWD 578: More about the function fusc.

Peter Luschny, Rational Trees and Binary Partitions.

Moritz A. Stern, Über eine zahlentheoretische Funktion, J. Reine Angew. Math., 55 (1858), 193-220.

EXAMPLE

The sequence splits into rows of length 2^k:

0,

1, 1,

2, 3, 1, 2,

3, 5, 2, 5, 3, 4, 1, 3,

4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 4,

...

The fractions are

0,

1/2, 1,

2/3, 3/2, 1/3, 2,

3/4, 5/3, 2/5, 5/2, 3/5, 4/3, 1/4, 3,

4/5, 7/4, 3/7, 8/3, 5/8, 7/5, 2/7, 7/2, 5/7, 8/5, 3/8, 7/3, 4/7, 5/4, 1/5, 4,

...

MAPLE

SternDijkstra := proc(L, p, n) local k, i, len, M; len := nops(L); M := L; k := n; while k > 0 do M[1+(k mod len)] := add(M[i], i = 1..len); k := iquo(k, len); od; op(p, M) end:

Ltree := proc(n) 5*2^simplify(floor(log[2](n+1))); SternDijkstra([0, 1], 1, n + 2 + %) / SternDijkstra([1, 0], 2, n + 2) end:

a := proc(n) 5*2^simplify(floor(log[2](n+1))); SternDijkstra([0, 1], 1, n + 2 + %) end:

MATHEMATICA

SternDijkstra[L_, p_, n_] := Module[{k, i, len, M}, len := Length[L]; M = L; k = n; While[k > 0, M[[1 + Mod[k, len]]] = Sum[M[[i]], {i, 1, len}]; k = Quotient[k, len]]; M[[p]]]; Ltree[n_] := With[{k = 5*2^Simplify[ Floor[ Log[2, n + 1]]]}, SternDijkstra[{0, 1}, 1, n + 2 + k]/ SternDijkstra[{1, 0}, 2, n + 2]]; a[0] = 0; a[n_] := With[{k = 5*2^Simplify[ Floor[ Log[2, n + 1]]]}, SternDijkstra[{1, 0}, 1, n + 2 + k]]; row[0] = {a[0]}; row[n_] := Table[a[k], {k, 2^n - 3, 2^(n+1) - 4}] // Reverse; Table[row[n], {n, 0, 6}] // Flatten (* Jean-François Alcover, Jul 26 2013, after Maple *)

CROSSREFS

Cf. A002487, A070879, A047679, A007306, A174980.

Sequence in context: A210530 A076645 A011448 * A067280 A167157 A238837

Adjacent sequences:  A174978 A174979 A174980 * A174982 A174983 A174984

KEYWORD

easy,nonn,frac,tabf

AUTHOR

Peter Luschny, Apr 03 2010

STATUS

approved

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Last modified September 22 00:25 EDT 2017. Contains 292326 sequences.