A184920 a(n) = n+[s*n/r]+[t*n/r]+[u*n/r], where []=floor and r=2^(1/2), s=r+1, t=r+2, u=r+3.

7, 15, 24, 31, 40, 48, 55, 64, 73, 82, 89, 97, 106, 113, 122, 130, 140, 147, 155, 164, 171, 180, 188, 195, 205, 213, 222, 229, 238, 246, 253, 262, 271, 280, 287, 295, 304, 311, 320, 328, 335, 345, 353, 362, 369, 378, 386, 393, 402, 411, 420, 427, 435, 444, 451, 460, 468, 478, 485, 493, 502, 509, 518, 526, 533, 543, 551, 560, 567, 575, 584, 591, 600, 608, 618, 625, 633, 642, 649, 658, 666, 673, 683, 691, 700, 707, 716, 724, 731, 740, 749, 758, 765, 773, 782, 789, 798, 806, 816, 823, 831, 840, 847, 856, 864, 871, 880, 889, 898, 905, 913, 922, 929, 938, 946, 956, 963, 971, 980, 987

Offset: 1

Author

Clark Kimberling, Jan 26 2011

Keywords

• nonn

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

Crossrefs

Cf. A184912, A184921, A184922, A184923.

Programs

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 *)