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%I #9 Apr 11 2021 01:31:17
%S 3,7,12,16,22,25,29,34,39,44,48,51,56,61,66,70,75,79,83,88,92,97,102,
%T 105,110,114,120,124,129,132,136,142,146,151,155,159,164,168,173,177,
%U 182,186,190,195,200,205,209,212,218,222,227,231,235,240,244,249,253,259,263,266,271,275,281,285,289,293,298,303,307,311,316,320,325,329,334,339,343,347,351,356,361,365,369,373,379,383,388,392,396,401,405,410,414,419,423,427,432,437,442,446,449,454,459,464,468,472,477,481,486,490,494,500,503,508,512,518,522,526,530,534
%N a(n) = n + [rn/t] + [sn/t] + [un/t], where []=floor and r=sin(Pi/2), s=sin(Pi/3), t=sin(Pi/4), u=sin(Pi/5).
%C The sequences A184924-A184928 partition the positive integers:
%C A184928: 1, 5, 6, 11, 14, 18, 21, 23, 27, ...
%C A184929: 2, 6, 10, 13, 17, 20, 24, 28, 32, ...
%C A184930: 3, 7, 12, 16, 22, 25, 29, 34, 39, ...
%C A184931: 4, 9, 15, 19, 26, 31, 36, 41, 47, ...
%C 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*t in the joint ranking is n + [rn/t] + [sn/t] + [un/t], and likewise for the positions of n*s, n*t, and n*u.
%t r=Sin[Pi/2]; s=Sin[Pi/3]; t=Sin[Pi/4]; u=Sin[Pi/5];
%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}] (* A184928 *)
%t Table[b[n],{n,1,120}] (* A184929 *)
%t Table[c[n],{n,1,120}] (* A184930 *)
%t Table[d[n],{n,1,120}] (* A184931 *)
%Y Cf. A184928, A184929, A184931.
%K nonn
%O 1,1
%A _Clark Kimberling_, Jan 26 2011
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