A184912 n+[ns/r]+[nt/r]+[nu/r], where []=floor and r=2^(1/5), s=r^2, t=r^3, u=r^4.

4, 9, 13, 19, 23, 28, 34, 39, 43, 49, 53, 58, 63, 69, 73, 79, 83, 88, 93, 98, 103, 109, 113, 118, 122, 128, 133, 138, 143, 148, 152, 158, 163, 168, 174, 178, 183, 188, 193, 197, 204, 208, 213, 218, 223, 227, 233, 238, 243, 247, 253, 257, 262, 268, 273, 277, 283, 287, 292, 297, 303, 307, 313, 318, 322, 328, 332, 338, 343, 348, 352, 358, 362, 368, 372, 378, 382, 387, 392, 397, 402, 408, 412, 417, 422, 427, 431, 438, 442, 447, 452, 457, 461, 467, 472, 477, 482, 487, 492, 496, 503, 507, 512, 517, 522, 526, 532, 537, 542, 547, 552, 556, 562, 566, 572, 577, 582, 586, 592, 596

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*r in the joint ranking is

n+[sn/r]+[tn/r]+[un/r], and likewise for the

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

Crossrefs

Cf. A184312, 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 *)

Formula

a(n)=n+[ns/r]+[nt/r]+[nu/r], where []=floor and

r=2^(1/5), s=r^2, t=r^3, u=r^4.