

A157271


Size of the largest set encompassing no {x, 2x} nor {x, 3x} contained in D(n) = the first n 3smooth numbers {1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27,...} (A003586).


2



1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 11, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 32, 32, 33, 33, 33, 34, 34, 35, 35
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OFFSET

1,3


COMMENTS

This is the strongly triplefree analog of A057561 and the description is modeled after A094708.
a(n) is the size of the maximal independent set in a grid graph with vertex set D(n) and edges connecting every x to 2x and every x to 3x.


LINKS

Giovanni Resta, Table of n, a(n) for n = 1..1000
J. Cassaigne and P. Zimmermann, Numerical Evaluation of the Strongly TripleFree Constant.
Julien Cassaigne and Paul Zimmermann, Numerical Evaluation of the Strongly TripleFree Constant (pdf file, 1996).
Steven R. Finch, TripleFree Sets of Integers [From Steven Finch, Apr 20 2019]


EXAMPLE

For n=7, the grid graph has rows {1,3,9}, {2,6}, {4}, {8} and the maximal set of nonadjacent vertices is {1,4,6,9}, hence a(7)=4.


MATHEMATICA

f[k_, n_]:=1+Floor[FullSimplify[Log[n/3^k]/Log[2]]]; g[n_]:=Floor[FullSimplify[Log[n]/Log[3]]]; peven[n_]:=Sum[Quotient[f[k, n]+Mod[k+1, 2], 2], {k, 0, g[n]}]; podd[n_]:=Sum[Quotient[f[k, n]+Mod[k, 2], 2], {k, 0, g[n]}]; p[n_]:=Max[peven[n], podd[n]]; v[1]=1; j=1; k=1; n=70; For[k=2, k<=n, k++, If[2*v[kj]<3^j, v[k]=2*v[kj], {v[k]=3^j, j++}]]; Table[p[v[n]], {n, 1, 70}] (* Steven Finch, Feb 27 2009; corrected by Giovanni Resta, Jul 29 2015 *)


CROSSREFS

Cf. A057561, A094708.
Sequence in context: A008619 A110654 A109728 * A025162 A248180 A025161
Adjacent sequences: A157268 A157269 A157270 * A157272 A157273 A157274


KEYWORD

nonn


AUTHOR

Steven Finch, Feb 26 2009


STATUS

approved



