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Search: id:A046947
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| A046947 |
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|sin(n)| (or |tan(n)| or |sec(n)|) decreases monotonically to 0; also |cos(n)| (or |cosec(n)| or |cot(n)|) increases. |
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+0
14
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| 1, 3, 22, 333, 355, 103993, 104348, 208341, 312689, 833719, 1146408, 4272943, 5419351, 80143857, 165707065, 245850922, 411557987, 1068966896, 2549491779, 6167950454, 14885392687, 21053343141, 1783366216531, 3587785776203
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Also numerators of convergents to Pi (A002486 gives denominators) beginning at 1.
Integer circumferences of circles with a(0)=1 and a(n+1) is the smallest integer circumference with corresponding diameter nearer an integer than is the diameter of the circle with circumference a(n). See PARI program. - Rick L. Shepherd (rshepherd2(AT)hotmail.com), Oct 06 2007
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REFERENCES
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K. H. Rosen et al., eds., Handbook of Discrete and Combinatorial Mathematics, CRC Press, 2000; p. 293.
Suggested by a question from Alan Walker (Alan_Walker(AT)sabre.com)
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LINKS
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Eric Weisstein's World of Mathematics, Cosecant
Eric Weisstein's World of Mathematics, Flint Hill Series
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EXAMPLE
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|sin(4272943)| = 0.000000549579497810490800503139..., |tan(4272943)| = 0.000000549579497810573797346111..., |sec(4272943)| = 1.00000000000015101881221...
|cos(4272943)| = 0.999999999999999270361852178903362129844..., |cosec(4272943)| = 0.00000181957297167010734684889..., |cot(4272943)| = 0.00000181957297166983255709999...
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MAPLE
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Digits := 50; M := 10000; a := [ 1 ]; R := sin(1.); for n from 2 to M do t1 := evalf(sin(n)); if abs(t1)<R then R := abs(t1); a := [ op(a), n ]; fi; od: a;
with(numtheory): cf := cfrac (Pi, 100): seq(nthnumer(cf, i), i=-1..22 ); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 07 2007
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MATHEMATICA
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z={}; current=1; Do[ If[ Abs[ Sin[ n]] < current, AppendTo[ z, current=Abs[ Sin[ n]]]], {n, 1, 10^7}]; z (* or *)
Join[{1}, Table[ Numerator[ FromContinuedFraction[ ContinuedFraction[Pi, n]]], {n, 1, 23}]]
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PROGRAM
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(PARI) /* Program calculates a(n) without using sin or continued fraction functions */ {d=1/Pi; print1("1, "); for(circum=2, 500000000, dm=circum/Pi; dmin=min(dm-floor(dm), ceil(dm)-dm); if(dmin<d, print1(circum, ", "); d=dmin))} /* or could use dmin=min(frac(dm), 1-frac(dm)) above */ - Rick L. Shepherd (rshepherd2(AT)hotmail.com), Oct 06 2007
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CROSSREFS
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Cf. A004112, A049946. See also A002485, which is the same sequence but begins at 0.
Sequence in context: A124567 A161967 A102223 this_sequence A002485 A099750 A156512
Adjacent sequences: A046944 A046945 A046946 this_sequence A046948 A046949 A046950
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms and Mathematica program from wouter.meeussen(AT)pandora.be. Further terms from Michel ten Voorde (seqfan(AT)tenvoorde.org)
Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 28 2003
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