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A172446 a(1) = 1, and for each k >=2, a(k) is the smallest number n such that n/cos(n) > a(k)/cos(a(k)), so that a(1)/cos(a(1)) > a(2)/cos(a(2)) > ... > a(k)/cos(a(k)) > ...

%I A172446 #18 Aug 16 2019 11:19:05
%S A172446 1,2,4,8,17,27,33,77,121,165,209,212,256,300,344,366,1054,1764,2474,
%T A172446 3184,3894,4604,5314,6024,6734,7444,8154,8864,9574,10284,10994,11704,
%U A172446 12414,13124,13834,14544,15254,15964,16674,17384,18094,18804,19514
%N A172446 a(1) = 1, and for each k >=2, a(k) is the smallest number n such that n/cos(n) > a(k)/cos(a(k)), so that a(1)/cos(a(1)) > a(2)/cos(a(2)) > ... > a(k)/cos(a(k)) > ...
%D A172446 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 83, p. 29, Ellipses, Paris 2008. Also Entry 137, p. 47.
%H A172446 Amiram Eldar, <a href="/A172446/b172446.txt">Table of n, a(n) for n = 1..100</a>
%e A172446 1/cos(1) = 1.850815..., 2/cos(2) = -4.805995..., 4/cos(4) = -6.119542...
%p A172446 a:= evalf(1/cos(1)); for n from 2 to 10000000 do; if a > evalf(n/cos(n)) then a:= evalf(n/cos(n)); print(n); else fi ; od;
%t A172446 s = {1}; rm = 1/Cos[1]; Do[r = n/Cos[n]; If[r < rm, rm = r; AppendTo[s, n]], {n, 2, 2*10^4}]; s (* _Amiram Eldar_, Aug 11 2019 *)
%Y A172446 Cf. A172448.
%K A172446 nonn
%O A172446 1,2
%A A172446 _Michel Lagneau_, Feb 03 2010
%E A172446 a(35) corrected by _Amiram Eldar_, Aug 11 2019