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 A189515 n+[ns]+[nt]; s=pi/2, t=2/pi. 3
 2, 6, 8, 12, 15, 18, 21, 25, 28, 31, 35, 37, 41, 43, 47, 51, 53, 57, 60, 63, 66, 70, 73, 76, 79, 82, 86, 88, 92, 96, 98, 102, 105, 108, 111, 114, 118, 121, 124, 127, 131, 133, 137, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 a(n)=n+[ns/r]+[nt/r], b(n)=n+[nr/s]+[nt/s], c(n)=n+[nr/t]+[ns/t], where []=floor. Taking r=1, s=pi/2, t=2/pi gives a=A189515, b=A189516, c=A189517. LINKS FORMULA a(n) = n+A140758(n) + floor(2*n/Pi). - R. J. Mathar, Sep 30 2011 MATHEMATICA r=1; s=Pi/2; t=2/Pi; a[n_] := n + Floor[n*s/r] + Floor[n*t/r]; b[n_] := n + Floor[n*r/s] + Floor[n*t/s]; c[n_] := n + Floor[n*r/t] + Floor[n*s/t]; Table[a[n], {n, 1, 120}]  (*A189515*) Table[b[n], {n, 1, 120}]  (*A189516*) Table[c[n], {n, 1, 120}]  (*A189517*) CROSSREFS Cf. A189516, A189517. Sequence in context: A276154 A138626 A178406 * A190344 A287000 A282358 Adjacent sequences:  A189512 A189513 A189514 * A189516 A189517 A189518 KEYWORD nonn AUTHOR Clark Kimberling, Apr 23 2011 STATUS approved

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Last modified July 23 20:44 EDT 2019. Contains 325264 sequences. (Running on oeis4.)