A184419 Lower s-Wythoff sequence, where s=lower Wythoff sequence. Complement of A184420.

1, 3, 4, 5, 7, 9, 10, 12, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29, 31, 32, 34, 35, 37, 38, 39, 41, 43, 44, 45, 47, 49, 50, 51, 53, 54, 56, 57, 59, 60, 62, 63, 65, 66, 68, 69, 70, 72, 74, 75, 76, 78, 79, 81, 83, 84, 85, 87, 88, 90, 91, 93, 94, 96, 97, 99, 100, 101, 103, 104, 106, 108, 109, 110, 112, 114, 115, 116, 118, 119, 121, 122, 124, 125, 127, 128, 130, 131, 133, 134, 135, 137, 139, 140, 141, 143, 144, 146, 148

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=(1,3,4,6,8,9,11,12,...)=A000201=lower Wythoff sequence;
a=(1,3,4,5,7,9,10,12,...)=A184419;
b=(2,6,8,11,15,18,21,24,...)=A184420.
Briefly: b=s+a, where a=mex="least missing".
		

Crossrefs

Cf. A184117, A000201, A184420.

Programs

Mathematica

mex:=First[Complement[Range[1,Max[#1]+1],#1]]&;
r=(1+5^(1/2))/2;s[n_]:=Floor[r*n];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,40}]
Table[a[n],{n,100}]
Table[b[n],{n,100}]