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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
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
KEYWORD
nonn,tabl
AUTHOR
Luc Rousseau, Jan 19 2019
STATUS
approved

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Last modified March 28 16:34 EDT 2024. Contains 371254 sequences. (Running on oeis4.)