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A172448 a(1) = 1, and for each n >=2, a(n) is the smallest number such that 1/cos(a(n)) < 1/cos(k) for all k < n, so that 1/cos(a(1)) > 1/cos(a(2)) > ... > 1/cos(a(n)) > ...

%I A172448 #17 Feb 16 2025 08:33:11
%S A172448 1,2,8,33,344,1054,1764,2474,3184,3894,4604,5314,6024,6734,7444,8154,
%T A172448 8864,9574,10284,10994,11704,12414,13124,13834,14544,15254,15964,
%U A172448 16674,17384,18094,18804,19514,20224,20934,21644,22354,23064,23774,24484
%N A172448 a(1) = 1, and for each n >=2, a(n) is the smallest number such that 1/cos(a(n)) < 1/cos(k) for all k < n, so that 1/cos(a(1)) > 1/cos(a(2)) > ... > 1/cos(a(n)) > ...
%D A172448 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 83, p. 29, Ellipses, Paris 2008. Also Entry 137, p. 47.
%H A172448 Amiram Eldar, <a href="/A172448/b172448.txt">Table of n, a(n) for n = 1..89</a>
%H A172448 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Pi.html">Pi</a>.
%e A172448 1/cos(1) = 1.8508157...,  1/cos(2) = -2.402997962...,  1/cos(8) = -6.8728506...
%p A172448 a:= evalf(1/ cos(1)); for n from 2 to 10000000 do; if a > evalf(1/cos(n)) then a:= evalf(1/cos(n)); print(n); else fi ; od;
%t A172448 am = 2; s = {}; Do[a = 1/Cos[n]; If[a < am, am = a; AppendTo[s, n]], {n, 1, 10^4}]; s (* _Amiram Eldar_, Aug 16 2019 *)
%Y A172448 Cf. A172446.
%K A172448 nonn
%O A172448 1,2
%A A172448 _Michel Lagneau_, Feb 03 2010