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Search: id:A141330
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| A141330 |
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a(n) = number of positive integers k, k < n, where the sine of k radians is < the sine of n radians. |
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+0
6
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| 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
(list; graph; listen)
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OFFSET
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1,6
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COMMENT
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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 (njas(AT)research.att.com), Oct 03 2008
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LINKS
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Diana Mecum, Table of n, a(n) for n = 1..1000
Leroy Quet, Home Page (listed in lieu of email address)
Robert Israel, Scatterplot of first 10000 terms
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CROSSREFS
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Cf. A141331, A141332, A141333, A141334, A141335.
Sequence in context: A100707 A078943 A063733 this_sequence A114375 A129200 A074958
Adjacent sequences: A141327 A141328 A141329 this_sequence A141331 A141332 A141333
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet Jun 25 2008
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EXTENSIONS
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More terms from Diana Mecum (diana.mecum(AT)gmail.com), Jul 14 2008
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