A184927 n+[rn/u]+[sn/u]+[tn/u], where []=floor and r=1, s=sqrt(3), t=sqrt(5), u=sqrt(7).

1, 4, 7, 10, 13, 16, 18, 22, 24, 27, 31, 33, 35, 39, 41, 45, 48, 50, 54, 56, 58, 62, 65, 68, 71, 73, 76, 79, 81, 85, 88, 91, 93, 96, 99, 102, 105, 108, 110, 114, 116, 119, 123, 125, 129, 131, 133, 137, 140, 142, 146, 148, 151, 154, 157, 160, 163, 165, 168, 171, 174, 177, 180, 183, 185, 188, 191, 194, 198, 200, 203, 206, 208, 211, 215, 217, 221, 223, 225, 229, 232, 234, 238, 239, 243, 246, 248, 252, 255, 258, 260, 263, 266, 269, 272, 275, 277, 281, 283, 286, 290, 292, 295, 298, 300, 304, 307, 309, 313, 315, 317, 321, 323, 327, 330, 332, 335, 338, 340, 344

Offset: 1

Author

Clark Kimberling, Jan 26 2011

Keywords

• nonn
• changed

Comments

The sequences A184924-A184927 partition the positive integers:

A184924: 6,14,21,28,37,44,52,59,...

A184925: 3,8,11,17,20,25,30,34,...

A184926: 2,5,9,12,15,19,23,26,29,...

A184927: 1,4,7,10,13,16,18,22,24,...

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*r, n*s, and n*t.

Crossrefs

Cf. A184924, A184925, A184926.

Programs

Mathematica

r=1; s=3^(1/2); t=5^(1/2); u=7^(1/2);
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}]  (* A184924 *)
Table[b[n],{n,1,120}]  (* A184925 *)
Table[c[n],{n,1,120}]  (* A184926 *)
Table[d[n],{n,1,120}]  (* A184927 *)
With[{c=Sqrt[7]},Table[n+Floor[n/c]+Floor[(n Sqrt[3])/c]+Floor[(n Sqrt[5])/c],{n,120}]] (* Harvey P. Dale, Aug 28 2025 *)

Extensions

Definition corrected by Georg Fischer, Jun 10 2020