A184923 n+[rn/u]+[sn/u]+[tn/u], where []=floor and r=2^(1/2), s=r+1, t=r+2, u=r+3.

1, 4, 6, 10, 11, 14, 17, 20, 21, 25, 28, 30, 34, 35, 38, 41, 44, 45, 49, 51, 54, 58, 59, 62, 65, 68, 69, 72, 75, 78, 79, 83, 86, 88, 92, 93, 96, 99, 102, 103, 107, 109, 112, 116, 117, 120, 123, 126, 127, 131, 133, 136, 137, 141, 144, 146, 150, 151, 154, 157, 160, 161, 165, 168, 170, 174, 175, 178, 181, 184, 185, 189, 191, 194, 198, 199, 202, 204, 208, 209, 212, 215, 218, 219, 223, 226, 228, 232, 233, 236, 239, 242, 243, 247, 249, 252, 256, 257, 260, 263, 266, 267, 270, 273, 276, 277, 281, 284, 286, 290, 291, 294, 297, 300, 301, 305, 307, 310, 314, 315

Offset

1,2

Comments

The sequences A184920-A184923 partition the positive integers:

A184920: 7,15,24,31,40,48,55,64,...

A184921: 3,8,13,18,23,27,32,37,...

A184922: 2,5,9,12,16,19,22,26,29,...

A184923: 1,4,6,10,11,14,17,20,21,...

Jointly rank the sets {h*r}, {i*s}, {j*t}, {k*u},

where h>=1, i>=1, j>=1, k>=1. The position of n*u in the joint ranking is n+[rn/u]+[sn/u]+[tn/u], and likewise for the positions of n*s, n*t, and n*u.

Links

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

Mathematica

r=2^(1/2); s=r+1; t=r+2; u=r+3);
a[n_]:=n+Floor[n*s/r]+Floor[n*t/r]+Floor[n*u/r];
b[n_]:=n+Floor[n*r/s]+Floor[n*t/s]+Floor[n*u/s];
c[n_]:=n+Floor[n*r/t]+Floor[n*s/t]+Floor[n*u/t];
d[n_]:=n+Floor[n*r/u]+Floor[n*s/u]+Floor[n*t/u];
Table[a[n], {n, 1, 120}]  (* A184920 *)
Table[b[n], {n, 1, 120}]  (* A184921 *)
Table[c[n], {n, 1, 120}]  (* A184922 *)
Table[d[n], {n, 1, 120}]  (* A184923 *)

Crossrefs

Cf. A184912, A184920, A184921, A184922.

Sequence in context: A110604 A109270 A187331 * A137877 A246022 A174240

Adjacent sequences: A184920 A184921 A184922 * A184924 A184925 A184926

Keyword

nonn

Author

Clark Kimberling, Jan 26 2011

Status

approved