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A172445 a(1) = 1, and for each k >=2, a(k) is the smallest number n such that n/sin(n) > a(k)/sin(a(k)), so that a(1)/sin(a(1)) > a(2)/sin(a(2)) > ... > a(k)/sin(a(k)) > ...

%I A172445 #13 Aug 11 2019 05:54:12
%S A172445 1,4,6,12,16,22,66,110,154,198,201,245,289,333,355,1065,1775,2485,
%T A172445 3195,3905,4615,5325,6035,6745,7455,8165,8875,9585,10295,11005,11715,
%U A172445 12425,13135,13845,14555,15265,15975,16685,17395,18105,18815,19525,20235
%N A172445 a(1) = 1, and for each k >=2, a(k) is the smallest number n such that n/sin(n) > a(k)/sin(a(k)), so that a(1)/sin(a(1)) > a(2)/sin(a(2)) > ... > a(k)/sin(a(k)) > ...
%D A172445 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 83, p. 29, Ellipses, Paris 2008. Also Entry 137, p. 47.
%H A172445 Amiram Eldar, <a href="/A172445/b172445.txt">Table of n, a(n) for n = 1..180</a>
%e A172445 1/sin(1) = 1.1883951..., 4/sin(4) = -5.285394..., 6/sin(6) = -21,473397...
%p A172445 a:= evalf(1/sin(1)); for n from 2 to 10000000 do; if a > evalf(n/sin(n)) then a:= evalf(n/sin(n)); print(n); else fi ; od;
%t A172445 s = {1}; rm = 1/Sin[1]; Do[r = n/Sin[n]; If[r < rm, rm = r; AppendTo[s, n]], {n, 2, 10^4}]; s (* _Amiram Eldar_, Aug 11 2019 *)
%K A172445 nonn
%O A172445 1,2
%A A172445 _Michel Lagneau_, Feb 03 2010