A184415 Lower s(n)-Wythoff sequence, where s(n)=floor[(n+2)/3]. Complement of A184416.

1, 3, 5, 7, 8, 11, 12, 14, 16, 18, 20, 21, 23, 26, 27, 29, 30, 33, 34, 37, 38, 40, 42, 43, 46, 47, 49, 52, 53, 54, 57, 59, 60, 61, 65, 66, 67, 69, 72, 74, 75, 76, 79, 81, 83, 84, 86, 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

Offset: 1

Author

Clark Kimberling, Jan 13 2011

Keywords

• nonn

Examples

			s=(1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,...)=A002264.
a=(1,3,5,7,8,11,12,14,16,18,20,...)=A184415.
b=(2,4,6,9,10,13,15,17,19,22,24,...)=A184416.
Briefly: s=a+b, where a=mex="least missing".
		

Crossrefs

Cf. A184117, A184416.

Programs

Mathematica

mex:=First[Complement[Range[1,Max[#1]+1],#1]]&;
s[n_]:=Floor[(n+2)/3];a[1]=1;b[n_]:=b[n]=s[n]+a[n];
a[n_]:=a[n]=mex[Flatten[Table[{a[i],b[i]},{i,1,n-1}]]];
Table[s[n],{n,20}]
Table[a[n],{n,100}]
Table[b[n],{n,100}]