A184921 n+[rn/s]+[tn/s]+[un/s], where []=floor and r=2^(1/2), s=r+1, t=r+2, u=r+3.

3, 8, 13, 18, 23, 27, 32, 37, 42, 47, 52, 56, 61, 66, 71, 76, 81, 85, 90, 95, 100, 105, 110, 114, 119, 124, 129, 134, 139, 143, 148, 153, 158, 163, 167, 172, 177, 182, 187, 192, 196, 201, 206, 211, 216, 221, 225, 230, 235, 240, 245, 250, 254, 259, 264, 269, 274, 279, 283, 288, 293, 298, 303, 308, 312, 317, 322, 327, 332, 336, 341, 346, 351, 356, 361, 365, 370, 375, 380, 385, 390, 394, 399, 404, 409, 414, 419, 423, 428, 433, 438, 443, 448, 452, 457, 462, 467, 472, 477, 481, 486, 491, 496, 501, 505, 510, 515, 520, 525, 530, 534, 539, 544, 549, 554, 559, 563, 568, 573, 578

Offset

1,1

Comments

The sequences A184920-A184923 partition the positive integers:

A184920: 7,15,24,31,40,48,55,64,...

A184921: 3,8,13,18,23,27,32,37,...

A184922: 2,5,9,12,16,19,22,26,29,...

A184923: 1,4,6,10,11,14,17,20,21,...

Jointly rank the sets {h*r}, {i*s}, {j*t}, {k*u},

where 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.

Links

Table of n, a(n) for n=1..120.

Mathematica

r=2^(1/2); s=r+1; t=r+2; u=r+3);
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}]  (* A184920 *)
Table[b[n], {n, 1, 120}]  (* A184921 *)
Table[c[n], {n, 1, 120}]  (* A184922 *)
Table[d[n], {n, 1, 120}]  (* A184923 *)

Crossrefs

Cf. A184912, A184920, A184922, A184923.

Sequence in context: A133330 A190505 A310305 * A282025 A310306 A095762

Adjacent sequences: A184918 A184919 A184920 * A184922 A184923 A184924

Keyword

nonn

Author

Clark Kimberling, Jan 26 2011

Status

approved