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

1,2

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=(1,1,2,2,3,3,4,4,5,5,6,6,7,7,...)=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".

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}]

Crossrefs

Cf. A184117, A184414.

Sequence in context: A087757 A188163 A088359 * A187345 A179185 A270198

Adjacent sequences: A184410 A184411 A184412 * A184414 A184415 A184416

Keyword

nonn

Author

Clark Kimberling, Jan 13 2011

Status

approved