A184480 Lower s-Wythoff sequence, where s(n)=3n. Complement of A001956.

1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 16, 18, 19, 20, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 35, 36, 37, 39, 40, 41, 42, 44, 45, 46, 48, 49, 50, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 65, 66, 67, 69, 70, 71, 72, 74, 75, 76, 78, 79, 80, 82, 83, 84, 85, 87, 88, 89, 91, 92, 93, 95, 96, 97, 99, 100, 101, 102, 104, 105, 106, 108, 109, 110, 112, 113, 114, 115, 117, 118, 119, 121, 122, 123, 125, 126, 127, 128, 130, 131, 132, 134, 135, 136, 138, 139, 140, 142, 143, 144, 145, 147, 148, 149, 151, 152, 153, 155, 156

Offset: 1

Author

Clark Kimberling, Jan 15 2011

Keywords

• nonn

Comments

A184480(n)=A001955(n) for n<43.

See A184117 for the definition of lower and upper Wythoff sequences.

Crossrefs

Cf. A184117.

Programs

Mathematica

k=3; r=0; d=Sqrt[4+k^2];
a[n_]:=Floor[(1/2)(d+2-k)(n+r/(d+2))];
b[n_]:=Floor[(1/2)(d+2+k)(n-r/(d+2))];
Table[a[n],{n,120}]
Table[b[n],{n,120}]

Formula

a(n)=floor[n*(-1+sqrt(13))/2].

b(n)=floor[n*(5+sqrt(13))/2]=A001956(n).