Search: id:A046947
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%I A046947
%S A046947 1,3,22,333,355,103993,104348,208341,312689,833719,1146408,4272943,
%T A046947 5419351,80143857,165707065,245850922,411557987,1068966896,2549491779,
%U A046947 6167950454,14885392687,21053343141,1783366216531,3587785776203
%N A046947 |sin(n)| (or |tan(n)| or |sec(n)|) decreases monotonically to 0; also 
               |cos(n)| (or |cosec(n)| or |cot(n)|) increases.
%C A046947 Also numerators of convergents to Pi (A002486 gives denominators) beginning 
               at 1.
%C A046947 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
%D A046947 K. H. Rosen et al., eds., Handbook of Discrete and Combinatorial Mathematics, 
               CRC Press, 2000; p. 293.
%D A046947 Suggested by a question from Alan Walker (Alan_Walker(AT)sabre.com)
%H A046947 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Cosecant.html">Cosecant</a>
%H A046947 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               FlintHillSeries.html">Flint Hill Series</a>
%e A046947 |sin(4272943)| = 0.000000549579497810490800503139..., |tan(4272943)| 
               = 0.000000549579497810573797346111..., |sec(4272943)| = 1.00000000000015101881221...
%e A046947 |cos(4272943)| = 0.999999999999999270361852178903362129844..., |cosec(4272943)| 
               = 0.00000181957297167010734684889..., |cot(4272943)| = 0.00000181957297166983255709999...
%p A046947 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;
%p A046947 with(numtheory): cf := cfrac (Pi,100): seq(nthnumer(cf,i), i=-1..22 ); 
               - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 07 2007
%t A046947 z={}; current=1; Do[ If[ Abs[ Sin[ n]] < current, AppendTo[ z, current=Abs[ 
               Sin[ n]]]], {n, 1, 10^7}]; z (* or *)
%t A046947 Join[{1}, Table[ Numerator[ FromContinuedFraction[ ContinuedFraction[Pi, 
               n]]], {n, 1, 23}]]
%o A046947 (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
%Y A046947 Cf. A004112, A049946. See also A002485, which is the same sequence but 
               begins at 0.
%Y A046947 Sequence in context: A124567 A161967 A102223 this_sequence A002485 A099750 
               A156512
%Y A046947 Adjacent sequences: A046944 A046945 A046946 this_sequence A046948 A046949 
               A046950
%K A046947 nonn,nice
%O A046947 0,2
%A A046947 N. J. A. Sloane (njas(AT)research.att.com).
%E A046947 More terms and Mathematica program from wouter.meeussen(AT)pandora.be. 
               Further terms from Michel ten Voorde (seqfan(AT)tenvoorde.org)
%E A046947 Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 28 
               2003

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