A184917 n+[rn/s]+[tn/s]+[un/s], where []=floor and r=1, s=2^(1/4), t=s^2, u=s^3.

3, 7, 12, 16, 21, 26, 29, 34, 38, 43, 48, 52, 56, 60, 65, 70, 75, 79, 82, 87, 91, 97, 101, 105, 110, 113, 119, 123, 128, 132, 136, 141, 145, 150, 154, 158, 164, 167, 172, 176, 180, 185, 190, 194, 198, 203, 207, 212, 217, 221, 225, 229, 234, 239, 243, 248, 251, 256, 261, 265, 270, 274, 278, 283, 287, 292, 296, 301, 306, 309, 314, 318, 323, 328, 333, 336, 340, 345, 349, 355, 359, 362, 367, 371, 377, 381, 386, 389, 393, 399, 403, 408, 412, 416, 420, 425, 430, 434, 439, 443, 447, 452, 456, 461, 465, 470, 474, 478, 483, 487, 492, 497, 501, 505, 509, 514, 519, 523, 528, 531

Offset: 1

Author

Clark Kimberling, Jan 26 2011

Keywords

• nonn

Comments

The sequences A184916-A184919 partition the positive integers:

A184916: 4,9,15,19,25,31,35,41,...

A184917: 3,7,12,16,21,26,29,34,...

A184918: 2,6,10,13,17,22,24,28,...

A184919: 1,5,8,11,14,18,20,23,27,...

The joint ranking method of A184812 is extended here to four numbers r,s,t,u, as follows: jointly rank the sets {h*r}, {i*s}, {j*t}, {k*u}, h>=1, i>=1, j>=1, k>=1.

The position of n*s in the joint ranking is

n+[rn/s]+[tn/s]+[un/s], and likewise for the

positions of n*r, n*t, and n*u.

Crossrefs

Cf. A184912, A184916, A184918, A184919.

Programs

Mathematica

r=1; s=2^(1/4); t=2^(1/2); u=2^(3/4);
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}]  (* A184916 *)
Table[b[n],{n,1,120}]  (* A184917 *)
Table[c[n],{n,1,120}]  (* A184918 *)
Table[d[n],{n,1,120}]  (* A184919 *)