A184926 n+[rn/t]+[sn/t]+[un/t], where []=floor and r=1, s=sqrt(3), t=sqrt(5), u=sqrt(7).

2, 5, 9, 12, 15, 19, 23, 26, 29, 32, 36, 40, 43, 46, 49, 53, 57, 60, 63, 66, 70, 74, 77, 80, 84, 87, 90, 94, 97, 101, 104, 107, 111, 115, 118, 121, 124, 127, 132, 134, 138, 141, 145, 149, 152, 155, 159, 162, 164, 169, 172, 176, 179, 182, 186, 190, 193, 195, 199, 202, 207, 210, 213, 216, 220, 224, 226, 230, 233, 237, 240, 244, 247, 251, 254, 256, 261, 264, 268, 270, 274, 278, 282, 285, 288, 291, 294, 299, 301, 305, 308, 312, 316, 319, 322, 325, 329, 331, 336, 339, 343, 346, 349, 353, 356, 360, 362, 366, 369, 374, 376, 380, 383, 386, 391, 393, 397, 400, 404, 406

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*t in the joint ranking is n+[rn/t]+[sn/t]+[un/t], and likewise for the positions of n*r, n*s, 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, A184925, A184927.

Sequence in context: A063957 A184579 A186274 * A342745 A189384 A184922

Adjacent sequences: A184923 A184924 A184925 * A184927 A184928 A184929

Keyword

nonn

Author

Clark Kimberling, Jan 26 2011

Status

approved