A172451 a(1) = 1, and for each n >= 2, a(n) is the smallest number such that 1/sin(a(n)) < 1/sin(a(k)) for all k < n, so that 1/sin(a(1)) > 1/sin(a(2)) > ... > 1/sin(a(n)) > ...
1, 2, 4, 6, 22, 333, 355, 103993, 104348, 1042060, 1146408, 4272943, 5419351, 80143857
Offset: 1
Examples
1/sin(1) = 1.1883951; 1/sin(2) = 1.0997501; 1/sin(4) = - 1.3213487.
References
- J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 83, p. 29, Ellipses, Paris 2008. Also Entry 137, p. 47.
Links
- Eric Weisstein's World of Mathematics, Pi
Programs
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Maple
a:= evalf(1/sin(1)); for n from 2 to 10000000 do; if a > evalf(1/sin(n)) then a:= evalf(1/sin(n)); print(n); else fi ; od;
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Mathematica
vm = 2; s = {}; Do[v = 1/Sin[n]; If[v < vm, vm = v; AppendTo[s, n]], {n, 1, 110000}]; s (* Amiram Eldar, Aug 10 2019 *) -
PARI
lista(NN) = {my(x=2); for(k=1, NN, if(1/sin(k)
Extensions
a(13) corrected and a(14) added by Amiram Eldar, Aug 10 2019