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A323607 Triangular array: row n is the list of numbers from 1 to n, sorted in Sharkovsky order. 2
1, 2, 1, 3, 2, 1, 3, 4, 2, 1, 3, 5, 4, 2, 1, 3, 5, 6, 4, 2, 1, 3, 5, 7, 6, 4, 2, 1, 3, 5, 7, 6, 8, 4, 2, 1, 3, 5, 7, 9, 6, 8, 4, 2, 1, 3, 5, 7, 9, 6, 10, 8, 4, 2, 1, 3, 5, 7, 9, 11, 6, 10, 8, 4, 2, 1, 3, 5, 7, 9, 11, 6, 10, 12, 8, 4, 2, 1, 3, 5, 7, 9, 11, 13, 6, 10, 12, 8, 4, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..91.

Luc Rousseau, Array plot of the first 250 rows of the triangle

Eric Weisstein's World of Mathematics, Sharkovsky's Theorem

EXAMPLE

Array begins:

  1

  2  1

  3  2  1

  3  4  2  1

  3  5  4  2  1

  3  5  6  4  2  1

  3  5  7  6  4  2  1

  3  5  7  6  8  4  2  1

  3  5  7  9  6  8  4  2  1

  3  5  7  9  6 10  8  4  2  1

  3  5  7  9 11  6 10  8  4  2  1

  3  5  7  9 11  6 10 12  8  4  2  1

MATHEMATICA

lt[x_, y_] := Module[

  {c, d, xx, yy, u, v},

  {c, d} = IntegerExponent[#, 2] & /@ {x, y};

  xx = x/2^c;

  yy = y/2^d;

  u = If[xx == 1, \[Infinity], c];

  v = If[yy == 1, \[Infinity], d];

  If[u != v, u < v, If[u == \[Infinity], c > d, xx < yy]]]

row[n_] := Sort[Range[n], lt]

row /@ Range[13] // Flatten

CROSSREFS

Cf. A323608.

Sequence in context: A211189 A194968 A194980 * A194959 A194921 A195079

Adjacent sequences:  A323604 A323605 A323606 * A323608 A323609 A323610

KEYWORD

nonn,tabl

AUTHOR

Luc Rousseau, Jan 19 2019

STATUS

approved

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Last modified June 19 03:38 EDT 2021. Contains 345125 sequences. (Running on oeis4.)