A184924 n+[sn/r]+[tn/r]+[un/r], where []=floor and r=1, s=sqrt(3), t=sqrt(5), u=sqrt(7).

6, 14, 21, 28, 37, 44, 52, 59, 67, 75, 83, 89, 98, 106, 112, 120, 128, 136, 143, 150, 158, 167, 173, 181, 189, 197, 204, 212, 219, 227, 235, 242, 250, 257, 265, 273, 280, 287, 296, 303, 311, 318, 326, 334, 341, 348, 357, 364, 371, 379, 387, 395, 402, 409, 417, 425, 432, 440, 448, 455, 463, 471, 478, 486, 493, 501, 509, 516, 524, 532, 538, 546, 555, 562, 569, 577, 585, 593, 600, 607, 616, 623, 630, 638, 646, 653, 661, 668, 677, 684, 691, 699, 707, 714, 722, 729, 737, 745, 752, 760, 767, 775, 783, 791, 797, 806, 814, 821, 828, 836, 844, 851, 858, 866, 875, 881, 889, 897, 905, 912

Offset

1,1

Comments

The sequences A184924-A184927 partition the positive integers:

A184924: 6,14,21,28,37,44,52,59,...

A184925: 3,8,11,17,20,25,30,34,...

A184926: 2,5,9,12,15,19,23,26,29,...

A184927: 1,4,7,10,13,16,18,22,24,...

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*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.

Links

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

Mathematica

r=1; s=3^(1/2); t=5^(1/2); u=7^(1/2);
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}]  (* A184924 *)
Table[b[n], {n, 1, 120}]  (* A184925 *)
Table[c[n], {n, 1, 120}]  (* A184926 *)
Table[d[n], {n, 1, 120}]  (* A184927 *)

Crossrefs

Cf. A184912, A184916, A184920, A184925, A184926, A184927.

Sequence in context: A122784 A244175 A063299 * A110223 A190504 A175582

Adjacent sequences: A184921 A184922 A184923 * A184925 A184926 A184927

Keyword

nonn

Author

Clark Kimberling, Jan 26 2011

Status

approved