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

1,2

Comments

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

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

Links

Table of n, a(n) for n=1..120.

Formula

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

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

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}]

Crossrefs

Cf. A184117.

Sequence in context: A276341 A098572 A001955 * A194375 A188222 A329990

Adjacent sequences: A184477 A184478 A184479 * A184481 A184482 A184483

Keyword

nonn

Author

Clark Kimberling, Jan 15 2011

Status

approved