Pensieve header: Figuring out wacky numbers, following Itai and Tsimerman.

WackyQ[1]=WackyQ[2]=True;
WackyQ[n_] /; n>2 := WackyQ[n] = Module[{k,ws=0},
For[k=1, k<n/2∧ws<2, ++k, If[WackyQ[k]∧WackyQ[n-k], ++ws]];
ws==1
];
WackyPi[1]=1;
WackyPi[n_] /; n>1 := WackyPi[n] = WackyPi[n-1]+If[WackyQ[n],1,0];

Select[Range[1000], WackyQ] // Length

ListLogLogPlot[Table[WackyPi[n], {n,1,1000}]]

ListLogLogPlot[Table[WackyPi[n], {n,1,50000,100}]]

((Log[WackyPi[50000]])/(Log[50000]))//N

With[{n=30000}, ((Log[WackyPi[n]])/(Log[n]))//N]

ListPlot[Table[(((1-((Log[WackyPi[n]])/(Log[n]))))^(-1)), {n,1000,50000,100}]]

ListLogLogPlot[Table[WackyPi[n], {n,1,250000,100}]]

((Log[WackyPi[250000]])/(Log[250000]))//N