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A189515 n+[ns]+[nt]; s=pi/2, t=2/pi. 3


%S 2,6,8,12,15,18,21,25,28,31,35,37,41,43,47,51,53,57,60,63,66,70,73,76,

%T 79,82,86,88,92,96,98,102,105,108,111,114,118,121,124,127,131,133,137,

%U 141,143,147,149,153,156,159,163,166,169,172,176,178,182,185,188,192,194,198,201,204,208,211,214,217,220,223,227,230,233,237,239,243,246,249,253,255,259,262,265

%N n+[ns]+[nt]; s=pi/2, t=2/pi.

%C This is one of three sequences that partition the positive integers. In general, suppose that r, s, t are positive real numbers for which the sets {i/r: i>=1}, {j/s: j>=1}, {k/t: k>=1} are pairwise disjoint. Let a(n) be the rank of n/r when all the numbers in the three sets are jointly ranked. Define b(n) and c(n) as the ranks of n/s and n/t. It is easy to prove that

%C a(n)=n+[ns/r]+[nt/r],

%C b(n)=n+[nr/s]+[nt/s],

%C c(n)=n+[nr/t]+[ns/t], where []=floor.

%C Taking r=1, s=pi/2, t=2/pi gives

%C a=A189515, b=A189516, c=A189517.

%F a(n) = n+A140758(n) + floor(2*n/Pi). - R. J. Mathar, Sep 30 2011

%t r=1; s=Pi/2; t=2/Pi;

%t a[n_] := n + Floor[n*s/r] + Floor[n*t/r];

%t b[n_] := n + Floor[n*r/s] + Floor[n*t/s];

%t c[n_] := n + Floor[n*r/t] + Floor[n*s/t];

%t Table[a[n], {n, 1, 120}] (*A189515*)

%t Table[b[n], {n, 1, 120}] (*A189516*)

%t Table[c[n], {n, 1, 120}] (*A189517*)

%Y Cf. A189516, A189517.

%K nonn

%O 1,1

%A _Clark Kimberling_, Apr 23 2011

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Last modified August 22 00:43 EDT 2019. Contains 326169 sequences. (Running on oeis4.)