A184931 a(n) = n + [rn/u] + [sn/u] + [tn/u], where []=floor and r=sin(Pi/2), s=sin(Pi/3), t=sin(Pi/4), u=sin(Pi/5).

4, 9, 15, 19, 26, 31, 36, 41, 47, 53, 58, 63, 69, 73, 80, 85, 90, 95, 100, 107, 111, 117, 122, 127, 133, 139, 143, 149, 154, 161, 165, 171, 176, 181, 187, 193, 197, 202, 208, 214, 219, 224, 230, 234, 241, 246, 251, 256, 262, 268, 273, 278, 284, 288, 295, 300, 304, 310, 315, 322, 326, 332, 337, 342, 348, 354, 358, 364, 370, 376, 380, 386, 391, 397, 402, 407, 413, 417, 424, 429, 434, 439, 445, 450, 456, 461, 467, 471, 478, 483, 488, 493, 499, 504, 509, 515, 520, 525, 531, 537, 541, 547, 552, 558, 563, 569, 574, 579, 585, 591, 595, 601, 606, 611, 617, 622, 628, 632, 639, 644

Offset

1,1

Comments

The sequences A184924-A184928 partition the positive integers:

A184928: 1, 5, 6, 11, 14, 18, 21, 23, 27, ...

A184929: 2, 6, 10, 13, 17, 20, 24, 28, 32, ...

A184930: 3, 7, 12, 16, 22, 25, 29, 34, 39, ...

A184931: 4, 9, 15, 19, 26, 31, 36, 41, 47, ...

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

Links

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

Mathematica

r=Sin[Pi/2]; s=Sin[Pi/3]; t=Sin[Pi/4]; u=Sin[Pi/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}]  (* A184928 *)
Table[b[n], {n, 1, 120}]  (* A184929 *)
Table[c[n], {n, 1, 120}]  (* A184930 *)
Table[d[n], {n, 1, 120}]  (* A184931 *)

Crossrefs

Cf. A184928, A184929, A184930.

Sequence in context: A313217 A313218 A313219 * A313220 A313221 A313222

Adjacent sequences: A184928 A184929 A184930 * A184932 A184933 A184934

Keyword

nonn

Author

Clark Kimberling, Jan 26 2011

Status

approved