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A184929 a(n) = n + [rn/s] + [tn/s] + [un/s], where []=floor and r=sin(Pi/2), s=sin(Pi/3), t=sin(Pi/4), u=sin(Pi/5).

%I A184929 #9 Apr 11 2021 01:31:06
%S A184929 2,6,10,13,17,20,24,28,32,35,38,42,46,50,54,57,60,64,67,72,76,78,82,
%T A184929 86,89,94,98,101,104,108,112,115,119,123,126,130,134,137,141,145,148,
%U A184929 152,156,158,162,167,170,174,178,180,184,189,192,196,199,203,206,210,215,217,221,225,228,232,237,239,243,247,250,254,257,261,265,269,272,276,279,283,287,291,294,297,301,305,309,313,317,319,323,327,331,335,338,341,345,349,353,357,360,363,367,371,374,378,382,385,389,393,395,400,404,408,411,415,418,421,426,430,433,436
%N A184929 a(n) = n + [rn/s] + [tn/s] + [un/s], where []=floor and r=sin(Pi/2), s=sin(Pi/3), t=sin(Pi/4), u=sin(Pi/5).
%C A184929 The sequences A184924-A184928 partition the positive integers:
%C A184929   A184928: 1, 5,  6, 11, 14, 18, 21, 23, 27, ...
%C A184929   A184929: 2, 6, 10, 13, 17, 20, 24, 28, 32, ...
%C A184929   A184930: 3, 7, 12, 16, 22, 25, 29, 34, 39, ...
%C A184929   A184931: 4, 9, 15, 19, 26, 31, 36, 41, 47, ...
%C A184929 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*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 A184929 r=Sin[Pi/2]; s=Sin[Pi/3]; t=Sin[Pi/4]; u=Sin[Pi/5];
%t A184929 a[n_]:=n+Floor[n*s/r]+Floor[n*t/r]+Floor[n*u/r];
%t A184929 b[n_]:=n+Floor[n*r/s]+Floor[n*t/s]+Floor[n*u/s];
%t A184929 c[n_]:=n+Floor[n*r/t]+Floor[n*s/t]+Floor[n*u/t];
%t A184929 d[n_]:=n+Floor[n*r/u]+Floor[n*s/u]+Floor[n*t/u];
%t A184929 Table[a[n],{n,1,120}]  (* A184928 *)
%t A184929 Table[b[n],{n,1,120}]  (* A184929 *)
%t A184929 Table[c[n],{n,1,120}]  (* A184930 *)
%t A184929 Table[d[n],{n,1,120}]  (* A184931 *)
%Y A184929 Cf. A184928, A184930, A184931.
%K A184929 nonn
%O A184929 1,1
%A A184929 _Clark Kimberling_, Jan 26 2011