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

1,2

Comments

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

Links

Table of n, a(n) for n=1..100.

Example

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".

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}]

Crossrefs

Cf. A184117, A000201, A184420.

Sequence in context: A183213 A183172 A136495 * A285970 A189665 A156246

Adjacent sequences: A184416 A184417 A184418 * A184420 A184421 A184422

Keyword

nonn

Author

Clark Kimberling, Jan 13 2011

Status

approved