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A184413 Lower s(n)-Wythoff sequence, where s(n)=floor[(n+1)/2]; complement of A184414.

%I A184413 #4 Mar 30 2012 18:57:13
%S A184413 1,3,5,6,9,10,11,14,16,17,19,20,23,24,27,28,29,32,33,34,37,39,40,42,
%T A184413 45,46,47,49,51,53,55,56,57,60,62,64,65,67,69,70,73,75,76,78,79,81,83,
%U A184413 85,87,88,91,92,93,95,97,99,101,103,105,106,108,110,111,114,115,116,119,121,123,124,126,128,129,131,133,134,137,138,140,142,144,145,147,150,151,152,154,156,157,160,161,163,165,167,169,170,173,174,175,178
%N A184413 Lower s(n)-Wythoff sequence, where s(n)=floor[(n+1)/2]; complement of A184414.
%C A184413 See A184117 for the definition of lower and upper s(n)-Wythoff sequences.
%e A184413 s=(1,1,2,2,3,3,4,4,5,5,6,6,7,7,...)=A004526;
%e A184413 a=(1,3,5,6,9,10,11,14,16,17,19,...)=A184413;
%e A184413 b=(2,4,7,8,12,13,15,18,21,22,25,...)=A184414;
%e A184413 Briefly: b=s+a; where a(n)=mex="least missing".
%t A184413 mex:=First[Complement[Range[1,Max[#1]+1],#1]]&;
%t A184413 s[n_]:=Floor[(n+1)/2];a[1]=1;b[n_]:=b[n]=s[n]+a[n];
%t A184413 a[n_]:=a[n]=mex[Flatten[Table[{a[i],b[i]},{i,1,n-1}]]];
%t A184413 Table[s[n],{n,20}]
%t A184413 Table[a[n],{n,100}]
%t A184413 Table[b[n],{n,100}]
%Y A184413 Cf. A184117, A184414.
%K A184413 nonn
%O A184413 1,2
%A A184413 _Clark Kimberling_, Jan 13 2011