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A184928 a(n) = n + [sn/r] + [tn/r] + [un/r], where []=floor and r=sin(Pi/2), s=sin(Pi/3), t=sin(Pi/4), u=sin(Pi/5).

%I A184928 #9 Apr 10 2021 23:54:58
%S A184928 1,5,8,11,14,18,21,23,27,30,33,37,40,43,45,49,52,55,59,62,65,68,71,74,
%T A184928 77,81,84,87,91,93,96,99,103,106,109,113,116,118,121,125,128,131,135,
%U A184928 138,140,144,147,150,153,157,160,163,166,169,172,175,179,183,185,188,191,194,198,201,204,207,211,213,216,220,223,226,229,233,236,238,242,245,248,252,255,258,260,264,267,270,274,277,280,282,286,290,292,296,299,302,306,308,312,314,318,321,324,328,330,333,336,340,344,346,350,352,355,359,362,366,368,372,375,377
%N A184928 a(n) = n + [sn/r] + [tn/r] + [un/r], where []=floor and r=sin(Pi/2), s=sin(Pi/3), t=sin(Pi/4), u=sin(Pi/5).
%C A184928 The sequences A184924-A184928 partition the positive integers:
%C A184928   A184928: 1, 5,  6, 11, 14, 18, 21, 23, 27, ...
%C A184928   A184929: 2, 6, 10, 13, 17, 20, 24, 28, 32, ...
%C A184928   A184930: 3, 7, 12, 16, 22, 25, 29, 34, 39, ...
%C A184928   A184931: 4, 9, 15, 19, 26, 31, 36, 41, 47, ...
%C A184928 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*r in the joint ranking is n + [sn/r] + [tn/r] + [un/r], and likewise for the positions of n*s, n*t, and n*u.
%t A184928 r=Sin[Pi/2]; s=Sin[Pi/3]; t=Sin[Pi/4]; u=Sin[Pi/5];
%t A184928 a[n_]:=n+Floor[n*s/r]+Floor[n*t/r]+Floor[n*u/r];
%t A184928 b[n_]:=n+Floor[n*r/s]+Floor[n*t/s]+Floor[n*u/s];
%t A184928 c[n_]:=n+Floor[n*r/t]+Floor[n*s/t]+Floor[n*u/t];
%t A184928 d[n_]:=n+Floor[n*r/u]+Floor[n*s/u]+Floor[n*t/u];
%t A184928 Table[a[n],{n,1,120}]  (* A184928 *)
%t A184928 Table[b[n],{n,1,120}]  (* A184929 *)
%t A184928 Table[c[n],{n,1,120}]  (* A184930 *)
%t A184928 Table[d[n],{n,1,120}]  (* A184931 *)
%Y A184928 Cf. A184929, A184930, A184931; also, A184912, A184916, A184920, A184924.
%K A184928 nonn
%O A184928 1,2
%A A184928 _Clark Kimberling_, Jan 26 2011