A184914 n+[rn/t]+[sn/t]+[un/t], where []=floor and r=2^(1/5), s=r^2, t=r^3, u=r^4.

2, 6, 10, 14, 17, 21, 26, 29, 32, 36, 40, 44, 47, 52, 56, 59, 62, 66, 70, 74, 78, 82, 86, 89, 92, 96, 101, 105, 108, 112, 115, 119, 123, 127, 131, 135, 139, 142, 145, 149, 154, 157, 161, 165, 169, 172, 175, 180, 184, 187, 191, 195, 199, 203, 206, 210, 214, 217, 221, 225, 230, 232, 236, 240, 244, 248, 251, 256, 260, 263, 266, 270, 274, 279, 282, 286, 290, 293, 296, 300, 305, 309, 312, 316, 319, 323, 326, 331, 335, 339, 342, 346, 349, 353, 357, 361, 365, 369, 373, 376, 380, 384, 388, 391, 395, 399, 403, 407, 410, 414, 418, 421, 425, 429, 434, 436, 440, 444, 448, 451

Offset: 1

Author

Clark Kimberling, Jan 25 2011

Keywords

• nonn

Comments

The sequences A184912-A184915 partition the positive integers:

A184912: 4,9,13,19,23,28,34,...

A184913: 3,7,11,16,20,24,30,...

A184914: 2,6,10,14,17,21,26,...

A184915: 1,5,8,12,15,18,22,...

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. A184812, A184912, A184913, A184915.

Programs

Mathematica

r=2^(1/5); s=2^(2/5); t=2^(3/5); u=2^(4/5);
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}]  (* A184912 *)
Table[b[n],{n,1,120}]  (* A184913 *)
Table[c[n],{n,1,120}]  (* A184914 *)
Table[d[n],{n,1,120}]  (* A184915 *)