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%I #9 Jun 10 2020 07:40:07
%S 1,4,7,10,13,16,18,22,24,27,31,33,35,39,41,45,48,50,54,56,58,62,65,68,
%T 71,73,76,79,81,85,88,91,93,96,99,102,105,108,110,114,116,119,123,125,
%U 129,131,133,137,140,142,146,148,151,154,157,160,163,165,168,171,174,177,180,183,185,188,191,194,198,200,203,206,208,211,215,217,221,223,225,229,232,234,238,239,243,246,248,252,255,258,260,263,266,269,272,275,277,281,283,286,290,292,295,298,300,304,307,309,313,315,317,321,323,327,330,332,335,338,340,344
%N n+[rn/u]+[sn/u]+[tn/u], where []=floor and r=1, s=sqrt(3), t=sqrt(5), u=sqrt(7).
%C The sequences A184924-A184927 partition the positive integers:
%C A184924: 6,14,21,28,37,44,52,59,...
%C A184925: 3,8,11,17,20,25,30,34,...
%C A184926: 2,5,9,12,15,19,23,26,29,...
%C A184927: 1,4,7,10,13,16,18,22,24,...
%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*r, n*s, and n*t.
%t r=1; s=3^(1/2); t=5^(1/2); u=7^(1/2);
%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}] (* A184924 *)
%t Table[b[n],{n,1,120}] (* A184925 *)
%t Table[c[n],{n,1,120}] (* A184926 *)
%t Table[d[n],{n,1,120}] (* A184927 *)
%Y Cf. A184924, A184925, A184926.
%K nonn
%O 1,2
%A _Clark Kimberling_, Jan 26 2011
%E Definition corrected by _Georg Fischer_, Jun 10 2020