A157271 Size of the largest set encompassing no {x, 2x} nor {x, 3x} contained in D(n) = the first n 3-smooth numbers {1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27,...} (A003586).
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
Offset: 1
Keywords
Examples
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.
Links
- Giovanni Resta, Table of n, a(n) for n = 1..1000
- J. Cassaigne and P. Zimmermann, Numerical Evaluation of the Strongly Triple-Free Constant.
- Julien Cassaigne and Paul Zimmermann, Numerical Evaluation of the Strongly Triple-Free Constant (pdf file, 1996).
- Steven R. Finch, Triple-Free Sets of Integers [From Steven Finch, Apr 20 2019]
Programs
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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[k-j]<3^j,v[k]=2*v[k-j],{v[k]=3^j,j++}]]; Table[p[v[n]],{n,1,70}] (* Steven Finch, Feb 27 2009; corrected by Giovanni Resta, Jul 29 2015 *)
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