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A184925 n+[rn/s]+[tn/s]+[un/s], where []=floor and r=1, s=sqrt(3), t=sqrt(5), u=sqrt(7).

%I A184925 #10 Jun 08 2020 17:04:22
%S A184925 3,8,11,17,20,25,30,34,38,42,47,51,55,61,64,69,72,78,82,86,92,95,100,
%T A184925 103,109,113,117,122,126,130,135,139,144,147,153,156,161,166,170,175,
%U A184925 178,184,187,192,196,201,205,209,214,218,222,228,231,236,241,245,249,253,259,262,267,271,276,279,284,289,293,297,302,306,310,314,320,324,328,333,337,342,345,351,354,359,363,368,372,377,381,385,389,394,399,403,408,412,416,420,426,429,434,438,443,446,451,456,460,464,469,473,477,483,487,491,495,500,504,508,513,518,521,526
%N A184925 n+[rn/s]+[tn/s]+[un/s], where []=floor and r=1, s=sqrt(3), t=sqrt(5), u=sqrt(7).
%C A184925 The sequences A184924-A184927 partition the positive integers:
%C A184925   A184924: 6,14,21,28,37,44,52,59,...
%C A184925   A184925: 3,8,11,17,20,25,30,34,...
%C A184925   A184926: 2,5,9,12,15,19,23,26,29,...
%C A184925   A184927: 1,4,7,10,13,16,18,22,24,...
%C A184925 Jointly rank the sets {h*r}, {i*s}, {j*t}, {k*u},
%C A184925 where h>=1, i>=1, j>=1, k>=1.  The position of n*s in the joint ranking is n+[rn/s]+[tn/s]+[un/s], and likewise for the positions of n*r, n*t, and n*u.
%t A184925 r=1; s=3^(1/2); t=5^(1/2); u=7^(1/2);
%t A184925 a[n_]:=n+Floor[n*s/r]+Floor[n*t/r]+Floor[n*u/r];
%t A184925 b[n_]:=n+Floor[n*r/s]+Floor[n*t/s]+Floor[n*u/s];
%t A184925 c[n_]:=n+Floor[n*r/t]+Floor[n*s/t]+Floor[n*u/t];
%t A184925 d[n_]:=n+Floor[n*r/u]+Floor[n*s/u]+Floor[n*t/u];
%t A184925 Table[a[n],{n,1,120}]  (* A184924 *)
%t A184925 Table[b[n],{n,1,120}]  (* A184925 *)
%t A184925 Table[c[n],{n,1,120}]  (* A184926 *)
%t A184925 Table[d[n],{n,1,120}]  (* A184927 *)
%Y A184925 Cf. A184924, A184926, A184927.
%K A184925 nonn
%O A184925 1,1
%A A184925 _Clark Kimberling_, Jan 26 2011