A184918 n+[rn/t]+[sn/t]+[un/t], where []=floor and r=1, s=2^(1/4), t=s^2, u=s^3.

2, 6, 10, 13, 17, 22, 24, 28, 32, 36, 40, 44, 47, 50, 54, 59, 63, 66, 69, 73, 76, 81, 85, 88, 92, 95, 100, 103, 107, 111, 114, 118, 122, 126, 129, 133, 138, 140, 144, 148, 151, 155, 160, 163, 166, 170, 174, 178, 182, 186, 189, 192, 197, 201, 204, 208, 211, 215, 219, 223, 227, 230, 233, 238, 241, 245, 249, 253, 257, 260, 264, 267, 271, 276, 280, 282, 286, 290, 293, 298, 302, 304, 308, 312, 317, 320, 324, 327, 330, 335, 339, 343, 346, 350, 353, 357, 361, 365, 369, 372, 376, 380, 383, 387, 391, 395, 398, 402, 406, 409, 414, 418, 421, 424, 428, 432, 436, 440, 444, 446

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*t in the joint ranking is

n+[rn/t]+[sn/t]+[un/t], and likewise for the

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

Crossrefs

Cf. A184912, A184916, A184917, 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 *)