A184415 - OEIS

%I #4 Mar 30 2012 18:57:13

%S 1,3,5,7,8,11,12,14,16,18,20,21,23,26,27,29,30,33,34,37,38,40,42,43,

%T 46,47,49,52,53,54,57,59,60,61,65,66,67,69,72,74,75,76,79,81,83,84,86,

%U 87,91,92,93,95,97,99,101,104,105,106,107,111,112,114,116,118,119,121,122,125,128,129,130,132,134,136,138,139,142,144,146,147,149,150,152,155,157,158,160,162,164,166,167,169,171,172,175,177,179,181,182,184

%N Lower s(n)-Wythoff sequence, where s(n)=floor[(n+2)/3].  Complement of A184416.

%e s=(1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,...)=A002264.

%e a=(1,3,5,7,8,11,12,14,16,18,20,...)=A184415.

%e b=(2,4,6,9,10,13,15,17,19,22,24,...)=A184416.

%e Briefly: s=a+b, where a=mex="least missing".

%t mex:=First[Complement[Range[1,Max[#1]+1],#1]]&;

%t s[n_]:=Floor[(n+2)/3];a[1]=1;b[n_]:=b[n]=s[n]+a[n];

%t a[n_]:=a[n]=mex[Flatten[Table[{a[i],b[i]},{i,1,n-1}]]];

%t Table[s[n],{n,20}]

%t Table[a[n],{n,100}]

%t Table[b[n],{n,100}]

%Y Cf. A184117, A184416.

%K nonn

%O 1,2

%A _Clark Kimberling_, Jan 13 2011