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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.

%I A184919 #6 Dec 01 2024 17:31:19
%S A184919 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 A184919 77,80,84,86,90,93,96,99,102,106,108,112,116,117,121,124,127,130,134,
%U A184919 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 A184919 n+[rn/u]+[sn/u]+[tn/u], where []=floor and r=1, s=2^(1/4), t=s^2, u=s^3.
%C A184919 The sequences A184916-A184919 partition the positive integers:
%C A184919   A184916: 4,9,15,19,25,31,35,41,...
%C A184919   A184917: 3,7,12,16,21,26,29,34,...
%C A184919   A184918: 2,6,10,13,17,22,24,28,...
%C A184919   A184919: 1,5,8,11,14,18,20,23,27,...
%C A184919 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 A184919 The position of n*u in the joint ranking is
%C A184919 n+[rn/u]+[sn/u]+[tn/u], and likewise for the
%C A184919 positions of n*r, n*s, and n*t.
%t A184919  r=1; s=2^(1/4); t=2^(1/2); u=2^(3/4);
%t A184919 a[n_]:=n+Floor[n*s/r]+Floor[n*t/r]+Floor[n*u/r];
%t A184919 b[n_]:=n+Floor[n*r/s]+Floor[n*t/s]+Floor[n*u/s];
%t A184919 c[n_]:=n+Floor[n*r/t]+Floor[n*s/t]+Floor[n*u/t];
%t A184919 d[n_]:=n+Floor[n*r/u]+Floor[n*s/u]+Floor[n*t/u];
%t A184919 Table[a[n],{n,1,120}]  (* A184916 *)
%t A184919 Table[b[n],{n,1,120}]  (* A184917 *)
%t A184919 Table[c[n],{n,1,120}]  (* A184918 *)
%t A184919 Table[d[n],{n,1,120}]  (* A184919 *)
%t A184919 Table[With[{s=Surd[2,4]},n+Floor[n/s^3]+Floor[(n*s)/s^3]+Floor[(n*s^2)/s^3]],{n,120}] (* _Harvey P. Dale_, Dec 01 2024 *)
%Y A184919 Cf. A184912, A184916, A184917, A184918.
%K A184919 nonn
%O A184919 1,2
%A A184919 _Clark Kimberling_, Jan 26 2011