A184925 n+[rn/s]+[tn/s]+[un/s], where []=floor and r=1, s=sqrt(3), t=sqrt(5), u=sqrt(7).

3, 8, 11, 17, 20, 25, 30, 34, 38, 42, 47, 51, 55, 61, 64, 69, 72, 78, 82, 86, 92, 95, 100, 103, 109, 113, 117, 122, 126, 130, 135, 139, 144, 147, 153, 156, 161, 166, 170, 175, 178, 184, 187, 192, 196, 201, 205, 209, 214, 218, 222, 228, 231, 236, 241, 245, 249, 253, 259, 262, 267, 271, 276, 279, 284, 289, 293, 297, 302, 306, 310, 314, 320, 324, 328, 333, 337, 342, 345, 351, 354, 359, 363, 368, 372, 377, 381, 385, 389, 394, 399, 403, 408, 412, 416, 420, 426, 429, 434, 438, 443, 446, 451, 456, 460, 464, 469, 473, 477, 483, 487, 491, 495, 500, 504, 508, 513, 518, 521, 526

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*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=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. A184924, A184926, A184927.

Sequence in context: A058572 A310283 A262290 * A294478 A154485 A105410

Adjacent sequences: A184922 A184923 A184924 * A184926 A184927 A184928

Keyword

nonn

Author

Clark Kimberling, Jan 26 2011

Status

approved