A184913 n+[rn/s]+[tn/s]+[un/s], where []=floor and r=2^(1/5), s=r^2, t=r^3, u=r^4.

3, 7, 11, 16, 20, 24, 30, 33, 37, 42, 46, 50, 55, 60, 64, 68, 72, 76, 81, 85, 90, 95, 99, 102, 106, 111, 116, 120, 125, 129, 132, 137, 141, 146, 151, 155, 159, 164, 167, 171, 177, 181, 185, 190, 194, 198, 202, 207, 211, 215, 220, 224, 228, 234, 237, 241, 246, 250, 254, 259, 264, 267, 272, 276, 280, 285, 289, 294, 299, 302, 306, 311, 315, 320, 324, 329, 333, 336, 341, 345, 350, 355, 359, 363, 367, 371, 375, 381, 385, 389, 394, 398, 401, 406, 411, 415, 419, 424, 428, 432, 437, 441, 445, 450, 454, 458, 463, 468, 471, 476, 480, 484, 489, 493, 498, 502, 506, 510, 515, 519

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*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. A184812, A184913, A184914, 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 *)