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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)) > ...

%I A172451 #26 Feb 16 2025 08:33:11
%S A172451 1,2,4,6,22,333,355,103993,104348,1042060,1146408,4272943,5419351,
%T A172451 80143857
%N 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)) > ...
%D A172451 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 83, p. 29, Ellipses, Paris 2008. Also Entry 137, p. 47.
%H A172451 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Pi.html">Pi</a>
%e A172451 1/sin(1) = 1.1883951; 1/sin(2) = 1.0997501; 1/sin(4) = - 1.3213487.
%p A172451 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;
%t A172451 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 *)
%o A172451 (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
%Y A172451 Cf. A002485, A046959, A046965, A046964, A172445, A172446.
%K A172451 nonn,more
%O A172451 1,2
%A A172451 _Michel Lagneau_, Feb 03 2010
%E A172451 a(13) corrected and a(14) added by _Amiram Eldar_, Aug 10 2019