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Search: id:A115787
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| A115787 |
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Floor((n+1)*pi)-Floor(n*pi). |
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+0
4
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| 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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The arithmetic mean 1/(n+1)*sum(a(k)|k=0...n) converges to pi. What is effectively the same: the Cesaro limit (C1) of a(n) is pi.
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REFERENCES
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Arithmetic means, Cesaro limit: Zeller, K. and Beekmann, W., Theorie der Limitierungsverfahren. Springer Verlag, Berlin, 1970.
G. H. Hardy. Divergent series. At the Clarendon Press, Oxford 1979.
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FORMULA
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a(n) = Floor((n+1)*pi)-Floor(n*pi), n>=0.
a(n)=A063438(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 10 2008]
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EXAMPLE
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a(6)=3 because 7*pi=21.99, 6*pi=18.85 and so a(6)=21-18;
a(7)=4 because 8*pi=25.13 and so a(7)=25-21;
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CROSSREFS
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Cf. A022844, A115788, A115789, A115790.
Sequence in context: A053388 A091786 A162844 this_sequence A105592 A083565 A063438
Adjacent sequences: A115784 A115785 A115786 this_sequence A115788 A115789 A115790
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KEYWORD
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nonn
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AUTHOR
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Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jan 31 2006
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