A184919 n+[rn/u]+[sn/u]+[tn/u], where []=floor and r=1, s=2^(1/4), t=s^2, u=s^3.

1, 5, 8, 11, 14, 18, 20, 23, 27, 30, 33, 37, 39, 42, 45, 49, 53, 55, 58, 61, 64, 68, 71, 74, 77, 80, 84, 86, 90, 93, 96, 99, 102, 106, 108, 112, 116, 117, 121, 124, 127, 130, 134, 137, 139, 143, 146, 149, 153, 156, 159, 161, 165, 169, 171, 175, 177, 181, 184, 187, 191, 193, 196, 200, 202, 206, 209, 213, 216, 218, 222, 224, 228, 232, 235, 237, 240, 244, 246, 250, 254, 255, 259, 262, 266, 269, 272, 275, 277, 281, 285, 288, 291, 294, 297, 300, 303, 307, 310, 313, 316, 319, 322, 325, 329, 332, 334, 338, 341, 344, 348, 351, 354, 356, 360, 363, 366, 370, 373, 375

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*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. A184912, A184916, A184917, A184918.

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 *)
Table[With[{s=Surd[2,4]},n+Floor[n/s^3]+Floor[(n*s)/s^3]+Floor[(n*s^2)/s^3]],{n,120}] (* Harvey P. Dale, Dec 01 2024 *)