A207673 n+[nr/s]+[nt/s], where []=floor, r=5, s=(1+sqrt(5))/2, t=1/s.

4, 8, 13, 17, 21, 26, 30, 35, 39, 43, 48, 53, 57, 62, 66, 71, 75, 79, 84, 88, 93, 97, 102, 107, 111, 115, 120, 124, 129, 133, 137, 142, 146, 151, 156, 160, 165, 169, 173, 178, 182, 187, 191, 195, 201, 205, 209, 214, 218, 223, 227, 231, 236, 240, 245

Offset

1,1

Comments

The sequences A207672, A207673, A208326 partition the positive integers. To generate them, jointly rank the sets {i/r}, {j/s}, {k*s}. The positions of n/r in the joint ranking form A207672, and likewise for the other sequences.

For a guide to related sequences and conjectures, see A206911.

Links

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

Mathematica

r = 5; s = GoldenRatio; t = 1/s;
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, 60}]  (* A207672 *)
Table[b[n], {n, 1, 60}]  (* A207673 *)
Table[c[n], {n, 1, 60}]  (* A208326 *)

Crossrefs

Cf. A206911, A207672, A208326.

Sequence in context: A311854 A311855 A172325 * A311856 A311857 A311858

Adjacent sequences: A207670 A207671 A207672 * A207674 A207675 A207676

Keyword

nonn

Author

Clark Kimberling, Feb 26 2012

Extensions

Definition corrected by Georg Fischer, Jun 10 2020

Status

approved