A086316 Decimal expansion of estimate of the strongly triple-free set constant.
6, 1, 3, 4, 7, 5, 2, 6, 9, 2, 0, 2, 2, 3, 4, 4, 1, 6, 0, 1, 8, 0, 4, 1, 6, 6, 3, 8
Offset: 0
Examples
0.613475269... 0.6134752692022344160180416638... - _Steven Finch_, Feb 25 2009
Links
- Steven R. Finch, Triple-Free Sets of Integers [From Steven Finch, Apr 20 2019]
- Julien Cassaigne and Paul Zimmermann, Numerical Evaluation of the Strongly Triple-Free Constant (1996). [From _Steven Finch_, Feb 25 2009]
- Julien Cassaigne and Paul Zimmermann, Numerical Evaluation of the Strongly Triple-Free Constant (pdf file, 1996).
- Eric Weisstein's World of Mathematics, Triple-Free Set
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=4001; For[k=2,k=n,k++,If[2*v[k-j]<3^j,v[k]=2*v[k-j],{v[k]=3^j,j++}]]; Sum[p[v[n]]*(1/v[n]-1/v[n+1]),{n,1,4000}]/3 (* Steven Finch, Feb 25 2009 *)
Extensions
More terms from Steven Finch, Feb 25 2009