A141330 a(n) = number of positive integers k, k < n, where the sine of k radians is < the sine of n radians.

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, 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, 19, 37, 56, 40, 22, 4, 15, 35, 56, 50, 30, 10, 10, 32, 54, 63, 40, 18, 4, 28, 52, 75, 50, 26

Offset

1,6

Comments

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

Links

Diana Mecum, Table of n, a(n) for n = 1..1000

Robert Israel, Scatterplot of first 10000 terms

Mathematica

Table[Count[Range[n - 1], k_ /; Sin[k] < Sin[n]], {n, 79}] (* Michael De Vlieger, Aug 19 2017 *)

Crossrefs

Cf. A141331, A141332, A141333, A141334, A141335.

Sequence in context: A078943 A063733 A187089 * A239324 A373166 A114375

Adjacent sequences: A141327 A141328 A141329 * A141331 A141332 A141333

Keyword

nonn,look

Author

Leroy Quet, Jun 25 2008

Extensions

More terms from Diana L. Mecum, Jul 14 2008

Status

approved