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%I #15 Aug 20 2017 10:03:08
%S 0,1,0,0,0,2,4,7,4,2,0,4,8,13,9,5,1,4,10,17,15,9,3,3,11,19,24,15,7,1,
%T 11,21,32,21,11,1,10,22,35,29,17,5,8,22,37,38,23,9,5,21,37,48,31,15,1,
%U 19,37,56,40,22,4,15,35,56,50,30,10,10,32,54,63,40,18,4,28,52,75,50,26
%N a(n) = number of positive integers k, k < n, where the sine of k radians is < the sine of n radians.
%C _Leroy Quet_ observed (Aug 01 2008) that the scatterplot produced by the "graph" display shows an interesting hexagonal pattern. Robert Israel (see link) noticed that this is more dramatic when one plots 10000 terms. Franklin T. Adams-Watters then commented as follows: "What we are looking at is basically a graphical representation of the continued fraction for pi (or more precisely, 2*pi). Robert Israel's graph is, I think, showing the famous good approximation pi ~ 355/113; the scatterplot seems to represent several convergents between 22/7 and 355/113.s" - _N. J. A. Sloane_, Oct 03 2008
%H Diana Mecum, <a href="/A141330/b141330.txt">Table of n, a(n) for n = 1..1000</a>
%H Robert Israel, <a href="/A141330/a141330.gif">Scatterplot of first 10000 terms</a>
%t Table[Count[Range[n - 1], k_ /; Sin[k] < Sin[n]], {n, 79}] (* _Michael De Vlieger_, Aug 19 2017 *)
%Y Cf. A141331, A141332, A141333, A141334, A141335.
%K nonn,look
%O 1,6
%A _Leroy Quet_, Jun 25 2008
%E More terms from _Diana L. Mecum_, Jul 14 2008
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