A184901 n+floor(ns/r)+floor(nt/r), where r=(1+sqrt(5))/2, s=r+1, t=r+2.

4, 9, 13, 18, 24, 28, 33, 37, 43, 48, 52, 57, 63, 67, 72, 76, 82, 87, 91, 96, 100, 106, 111, 115, 120, 126, 130, 135, 139, 145, 150, 154, 159, 165, 169, 174, 178, 183, 189, 193, 198, 202, 208, 213, 217, 222, 228, 232, 237, 241, 247, 252, 256, 261, 265

Offset

1,1

Comments

This is one of three sequences, along with A016789 and A184903, that partition the positive integers; see A184812.

Links

Table of n, a(n) for n=1..55.

Formula

a(n)=n+floor(ns/r)+floor(nt/r), where r=(1+sqrt(5))/2, s=r+1, t=r+2.

Mathematica

r=(1+5^(1/2))/2; s=(3+5^(1/2))/2; t=(5+5^(1/2))/2;
a[n_]:=n+Floor [n*s/r]+Floor[n*t/r];
b[n_]:=n+Floor [n*r/s]+Floor[n*t/s];
c[n_]:=n+Floor[n*r/t]+Floor[n*s/t];
Table[a[n], {n, 1, 120}]  (* A184901 *)
Table[b[n], {n, 1, 120}]  (* A016789 *)
Table[c[n], {n, 1, 120}]  (* A184903 *)

Crossrefs

Cf. A016789, A184812, A184903.

Sequence in context: A312958 A312959 A312960 * A312961 A312962 A312963

Adjacent sequences: A184898 A184899 A184900 * A184902 A184903 A184904

Keyword

nonn

Author

Clark Kimberling, Jan 25 2011

Status

approved