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

1,2

Links

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

Example

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".

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}]

Crossrefs

Cf. A184117, A184416.

Sequence in context: A190719 A187224 A106252 * A050111 A090542 A260518

Adjacent sequences: A184412 A184413 A184414 * A184416 A184417 A184418

Keyword

nonn

Author

Clark Kimberling, Jan 13 2011

Status

approved