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)) > ...

1, 2, 8, 33, 344, 1054, 1764, 2474, 3184, 3894, 4604, 5314, 6024, 6734, 7444, 8154, 8864, 9574, 10284, 10994, 11704, 12414, 13124, 13834, 14544, 15254, 15964, 16674, 17384, 18094, 18804, 19514, 20224, 20934, 21644, 22354, 23064, 23774, 24484

Offset: 1

Author

Michel Lagneau, Feb 03 2010

Keywords

• nonn

Examples

			1/cos(1) = 1.8508157...,  1/cos(2) = -2.402997962...,  1/cos(8) = -6.8728506...
		

References

• J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 83, p. 29, Ellipses, Paris 2008. Also Entry 137, p. 47.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..89
• Eric Weisstein's World of Mathematics, Pi.

Crossrefs

Cf. A172446.

Programs

Maple

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;

Mathematica

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 *)