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 A184919 n+[rn/u]+[sn/u]+[tn/u], where []=floor and r=1, s=2^(1/4), t=s^2, u=s^3. 4

%I #4 Mar 30 2012 18:57:17

%S 1,5,8,11,14,18,20,23,27,30,33,37,39,42,45,49,53,55,58,61,64,68,71,74,

%T 77,80,84,86,90,93,96,99,102,106,108,112,116,117,121,124,127,130,134,

%U 137,139,143,146,149,153,156,159,161,165,169,171,175,177,181,184,187,191,193,196,200,202,206,209,213,216,218,222,224,228,232,235,237,240,244,246,250,254,255,259,262,266,269,272,275,277,281,285,288,291,294,297,300,303,307,310,313,316,319,322,325,329,332,334,338,341,344,348,351,354,356,360,363,366,370,373,375

%N n+[rn/u]+[sn/u]+[tn/u], where []=floor and r=1, s=2^(1/4), t=s^2, u=s^3.

%C The sequences A184916-A184919 partition the positive integers:

%C A184916: 4,9,15,19,25,31,35,41,...

%C A184917: 3,7,12,16,21,26,29,34,...

%C A184918: 2,6,10,13,17,22,24,28,...

%C A184919: 1,5,8,11,14,18,20,23,27,...

%C The joint ranking method of A184812 is extended here to four numbers r,s,t,u, as follows: jointly rank the sets {h*r}, {i*s}, {j*t}, {k*u}, h>=1, i>=1, j>=1, k>=1.

%C The position of n*u in the joint ranking is

%C n+[rn/u]+[sn/u]+[tn/u], and likewise for the

%C positions of n*r, n*s, and n*t.

%t r=1; s=2^(1/4); t=2^(1/2); u=2^(3/4);

%t a[n_]:=n+Floor[n*s/r]+Floor[n*t/r]+Floor[n*u/r];

%t b[n_]:=n+Floor[n*r/s]+Floor[n*t/s]+Floor[n*u/s];

%t c[n_]:=n+Floor[n*r/t]+Floor[n*s/t]+Floor[n*u/t];

%t d[n_]:=n+Floor[n*r/u]+Floor[n*s/u]+Floor[n*t/u];

%t Table[a[n],{n,1,120}] (* A184916 *)

%t Table[b[n],{n,1,120}] (* A184917 *)

%t Table[c[n],{n,1,120}] (* A184918 *)

%t Table[d[n],{n,1,120}] (* A184919 *)

%Y Cf. A184912, A184916, A184917, A184918.

%K nonn

%O 1,2

%A _Clark Kimberling_, Jan 26 2011

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