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A046947 |sin(n)| (or |tan(n)| or |sec(n)|) decreases monotonically to 0; also |cos(n)| (or |cosec(n)| or |cot(n)|) increases. 16
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; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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, Oct 06 2007

REFERENCES

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)

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..1946

Nelson A. Carella, Irrationality Measure of Pi, arXiv:1902.08817 [math.GM], 2019.

Eric Weisstein's World of Mathematics, Cosecant

Eric Weisstein's World of Mathematics, Flint Hills Series

EXAMPLE

|sin(4272943)| = 0.000000549579497810490800503139..., |tan(4272943)| = 0.000000549579497810573797346111..., |sec(4272943)| = 1.00000000000015101881221...

|cos(4272943)| = 0.999999999999848981187793172965367089856..., |cosec(4272943)| = 1819572.97167010734684889..., |cot(4272943)| = 1819572.97166983255709999...

MAPLE

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, Feb 07 2007

MATHEMATICA

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}]] (* Wouter Meeussen *)

Join[{1}, Convergents[Pi, 30]//Numerator] (* Harvey P. Dale, May 05 2019 *)

PROG

(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, Oct 06 2007

CROSSREFS

Cf. A004112, A049946. See also A002485, which is the same sequence but begins at 0.

Sequence in context: A102223 A189897 A306578 * A002485 A193193 A099750

Adjacent sequences:  A046944 A046945 A046946 * A046948 A046949 A046950

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Wouter Meeussen

Further terms from Michel ten Voorde

Edited and extended by Robert G. Wilson v, Jan 28 2003

Typo in examples fixed by Paolo Bonzini, Mar 21 2012

STATUS

approved

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Last modified November 13 12:45 EST 2019. Contains 329094 sequences. (Running on oeis4.)