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

1, 3, 5, 6, 9, 10, 11, 14, 16, 17, 19, 20, 23, 24, 27, 28, 29, 32, 33, 34, 37, 39, 40, 42, 45, 46, 47, 49, 51, 53, 55, 56, 57, 60, 62, 64, 65, 67, 69, 70, 73, 75, 76, 78, 79, 81, 83, 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

Offset: 1

Author

Clark Kimberling, Jan 13 2011

Keywords

• nonn

Comments

See A184117 for the definition of lower and upper s(n)-Wythoff sequences.

Examples

			s=(1,1,2,2,3,3,4,4,5,5,6,6,7,7,...)=A004526;
a=(1,3,5,6,9,10,11,14,16,17,19,...)=A184413;
b=(2,4,7,8,12,13,15,18,21,22,25,...)=A184414;
Briefly: b=s+a; where a(n)=mex="least missing".
		

Crossrefs

Cf. A184117, A184414.

Programs

Mathematica

mex:=First[Complement[Range[1,Max[#1]+1],#1]]&;
s[n_]:=Floor[(n+1)/2];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}]