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

1,2

References

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

Links

Table of n, a(n) for n=1..14.

Eric Weisstein's World of Mathematics, Pi

Example

1/sin(1) = 1.1883951; 1/sin(2) = 1.0997501; 1/sin(4) = - 1.3213487.

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;

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 *)

Prog

(PARI) lista(NN) = {my(x=2); for(k=1, NN, if(1/sin(k)<x, x=1/sin(k); print1(k", "))); } \\ Jinyuan Wang, Aug 12 2019

Crossrefs

Cf. A002485, A046959, A046965, A046964, A172445, A172446.

Sequence in context: A152482 A045960 A028988 * A335009 A086172 A261832

Adjacent sequences: A172448 A172449 A172450 * A172452 A172453 A172454

Keyword

nonn,more

Author

Michel Lagneau, Feb 03 2010

Extensions

a(13) corrected and a(14) added by Amiram Eldar, Aug 10 2019

Status

approved