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%I #46 Jun 20 2022 12:11:03
%S 0,1,2,5,8,11,344,699,1054,1409,1764,2119,2474,2829,3184,3539,3894,
%T 4249,4604,4959,5314,5669,6024,6379,6734,7089,7444,7799,8154,8509,
%U 8864,9219,9574,9929,10284,10639,10994,11349,11704,12059,12414,12769,13124,13479,13834
%N Numbers k where |cos(k)| (or |cosec(k)| or |cot(k)|) decreases monotonically to 0; also |tan(k)|, |sec(k)|, |sin(k)| increases.
%C a(167) > 10^10. - _Robert G. Wilson v_, Nov 04 2019
%C a(100), a(1000), and a(10000) have 5, 215, and 221 digits, respectively. - _Jon E. Schoenfield_, Nov 08 2019
%C a(n) is also the smallest nonnegative integer k such that k mod Pi is closer to Pi/2 than any previous term. - _Colin Linzer_, Apr 27 2022
%H Jon E. Schoenfield, <a href="/A004112/b004112.txt">Table of n, a(n) for n = 1..1000</a> (first 166 terms from Robert G. Wilson v)
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FlintHillsSeries.html">Flint Hills Series</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Secant.html">Secant</a>
%e After 151st term, the sequence continues 51819, 52174, 260515, 573204, 4846147, ...
%e |cos(4846147)| = 0.000000255689511369808141413171..., |cosec(4846147)| = 1.00000000000003268856311..., or |cot(4846147)| = 0.000000255689511369816499535901...
%e |tan(4846147)| = 3910993.43356970986068082..., |sec(4846147)| = 3910993.43356983770543651..., |sin(4846147)| = 0.999999999999967311436888...
%t a = -1; Do[b = N[ Abs[ Tan[n]], 24]; If[b > a, Print[n]; a = b], {n, 0, 13833}]
%o (PARI) e=2;for(n=0,1e9,abs(cos(n))<e & !print1(n",") & e=abs(cos(n))) \\ _M. F. Hasler_, Apr 01 2013
%Y Cf. A046947, A046956, A002485, A024814.
%K nonn,nice
%O 1,3
%A _Clark Kimberling_
%E More terms from _Olivier Gérard_
%E Edited by _Robert G. Wilson v_, Jan 28 2003
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