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
Carlos Hernan Lopez Zapata and Nikos Mantzakouras, Diophantine Flint-Hills series: convergence, polylogarithms and pi's bound, ResearchGate (2025). See pp. 6, 69.
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
KEYWORD
nonn,nice
AUTHOR
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