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)) > ...
1, 2, 4, 8, 17, 27, 33, 77, 121, 165, 209, 212, 256, 300, 344, 366, 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
Offset: 1
Keywords
Examples
1/cos(1) = 1.850815..., 2/cos(2) = -4.805995..., 4/cos(4) = -6.119542...
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..100
Crossrefs
Cf. A172448.
Programs
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Maple
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;
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Mathematica
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 *)
Extensions
a(35) corrected by Amiram Eldar, Aug 11 2019