A207672 n + [ns/r] + [nt/r], where []=floor, r=5, s=(1+sqrt(5))/2, t=1/s.

1, 2, 3, 5, 6, 7, 9, 10, 12, 14, 15, 16, 18, 19, 20, 22, 24, 25, 27, 28, 29, 31, 32, 33, 36, 37, 38, 40, 41, 42, 44, 45, 47, 49, 50, 51, 52, 54, 55, 56, 59, 60, 61, 63, 64, 65, 67, 68, 70, 72, 73, 74, 76, 77, 78, 80, 82, 83, 85, 86, 87, 89, 90, 91, 94, 95, 96, 98

Offset

1,2

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 a conjecture, see A206911.

Links

Table of n, a(n) for n=1..68.

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, A207673, A208326.

Sequence in context: A230391 A284931 A248229 * A038161 A158746 A062470

Adjacent sequences: A207669 A207670 A207671 * A207673 A207674 A207675

Keyword

nonn

Author

Clark Kimberling, Feb 26 2012

Status

approved