A208326 -id:A208326 - cp's OEIS frontend

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

Clark Kimberling, Feb 26 2012

nonn

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.

Cf. A206911, A207673, A208326.

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 *)

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

Original entry on oeis.org

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

Clark Kimberling, Feb 26 2012

nonn

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

Cf. A206911, A207672, A208326.

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 *)

Definition corrected by Georg Fischer, Jun 10 2020

cp's OEIS Frontend

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

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