This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A189781 n+[nr/s]+[nt/s]; r=pi/2, s=arcsin(8/17), t=arcsin(15/17). 4
 6, 12, 18, 24, 32, 38, 44, 50, 56, 64, 70, 76, 82, 88, 96, 102, 108, 114, 120, 128, 134, 140, 146, 152, 160, 166, 172, 178, 184, 192, 198, 204, 210, 218, 224, 230, 236, 242, 250, 256, 262, 268, 274, 282, 288, 294, 300, 306, 314, 320, 326, 332, 338, 346, 352, 358, 364, 370, 378, 384, 390, 396, 402, 410, 416, 422, 428, 436, 442, 448, 454, 460, 468 (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=pi/2, s=arcsin(8/17), t=arcsin(15/17) gives a=A005408, b=A189781, c=A189782.  Note that r=s+t. LINKS MATHEMATICA r=Pi/2; s=ArcSin[8/17]; t=ArcSin[15/17]; 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}]  (*A005408*) Table[b[n], {n, 1, 120}]  (*A189781*) Table[c[n], {n, 1, 120}]  (*A189782*) Table[b[n]/2, {n, 1, 120}]  (*A189783*) Table[c[n]/2, {n, 1, 120}]  (*A189784*) CROSSREFS Cf. A189782, A189783=(A189781)/2, A189784. Sequence in context: A037230 A277723 A033018 * A182302 A244193 A215142 Adjacent sequences:  A189778 A189779 A189780 * A189782 A189783 A189784 KEYWORD nonn AUTHOR Clark Kimberling, Apr 27 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 17 19:16 EDT 2019. Contains 327137 sequences. (Running on oeis4.)