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A184931 a(n) = n + [rn/u] + [sn/u] + [tn/u], where []=floor and r=sin(Pi/2), s=sin(Pi/3), t=sin(Pi/4), u=sin(Pi/5).

%I A184931 #10 Apr 11 2021 02:58:29
%S A184931 4,9,15,19,26,31,36,41,47,53,58,63,69,73,80,85,90,95,100,107,111,117,
%T A184931 122,127,133,139,143,149,154,161,165,171,176,181,187,193,197,202,208,
%U A184931 214,219,224,230,234,241,246,251,256,262,268,273,278,284,288,295,300,304,310,315,322,326,332,337,342,348,354,358,364,370,376,380,386,391,397,402,407,413,417,424,429,434,439,445,450,456,461,467,471,478,483,488,493,499,504,509,515,520,525,531,537,541,547,552,558,563,569,574,579,585,591,595,601,606,611,617,622,628,632,639,644
%N A184931 a(n) = n + [rn/u] + [sn/u] + [tn/u], where []=floor and r=sin(Pi/2), s=sin(Pi/3), t=sin(Pi/4), u=sin(Pi/5).
%C A184931 The sequences A184924-A184928 partition the positive integers:
%C A184931   A184928: 1, 5,  6, 11, 14, 18, 21, 23, 27, ...
%C A184931   A184929: 2, 6, 10, 13, 17, 20, 24, 28, 32, ...
%C A184931   A184930: 3, 7, 12, 16, 22, 25, 29, 34, 39, ...
%C A184931   A184931: 4, 9, 15, 19, 26, 31, 36, 41, 47, ...
%C A184931 Jointly rank the sets {h*r}, {i*s}, {j*t}, {k*u}, 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 A184931 r=Sin[Pi/2]; s=Sin[Pi/3]; t=Sin[Pi/4]; u=Sin[Pi/5];
%t A184931 a[n_]:=n+Floor[n*s/r]+Floor[n*t/r]+Floor[n*u/r];
%t A184931 b[n_]:=n+Floor[n*r/s]+Floor[n*t/s]+Floor[n*u/s];
%t A184931 c[n_]:=n+Floor[n*r/t]+Floor[n*s/t]+Floor[n*u/t];
%t A184931 d[n_]:=n+Floor[n*r/u]+Floor[n*s/u]+Floor[n*t/u];
%t A184931 Table[a[n],{n,1,120}]  (* A184928 *)
%t A184931 Table[b[n],{n,1,120}]  (* A184929 *)
%t A184931 Table[c[n],{n,1,120}]  (* A184930 *)
%t A184931 Table[d[n],{n,1,120}]  (* A184931 *)
%Y A184931 Cf. A184928, A184929, A184930.
%K A184931 nonn
%O A184931 1,1
%A A184931 _Clark Kimberling_, Jan 26 2011