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%I #4 Mar 30 2012 18:57:17
%S 1,4,6,10,11,14,17,20,21,25,28,30,34,35,38,41,44,45,49,51,54,58,59,62,
%T 65,68,69,72,75,78,79,83,86,88,92,93,96,99,102,103,107,109,112,116,
%U 117,120,123,126,127,131,133,136,137,141,144,146,150,151,154,157,160,161,165,168,170,174,175,178,181,184,185,189,191,194,198,199,202,204,208,209,212,215,218,219,223,226,228,232,233,236,239,242,243,247,249,252,256,257,260,263,266,267,270,273,276,277,281,284,286,290,291,294,297,300,301,305,307,310,314,315
%N n+[rn/u]+[sn/u]+[tn/u], where []=floor and r=2^(1/2), s=r+1, t=r+2, u=r+3.
%C The sequences A184920-A184923 partition the positive integers:
%C A184920: 7,15,24,31,40,48,55,64,...
%C A184921: 3,8,13,18,23,27,32,37,...
%C A184922: 2,5,9,12,16,19,22,26,29,...
%C A184923: 1,4,6,10,11,14,17,20,21,...
%C Jointly rank the sets {h*r}, {i*s}, {j*t}, {k*u},
%C 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*s, n*t, and n*u.
%t r=2^(1/2); s=r+1; t=r+2; u=r+3);
%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}] (* A184920 *)
%t Table[b[n],{n,1,120}] (* A184921 *)
%t Table[c[n],{n,1,120}] (* A184922 *)
%t Table[d[n],{n,1,120}] (* A184923 *)
%Y Cf. A184912, A184920, A184921, A184922.
%K nonn
%O 1,2
%A _Clark Kimberling_, Jan 26 2011
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