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Search: id:A143608
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| A143608 |
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Numerators of the lower principal and intermediate convergents to 2^(1/2). |
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+0
5
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| 1, 4, 7, 24, 41, 140, 239, 816, 1393, 4756, 8119, 27720, 47321, 161564, 275807, 941664, 1607521, 5488420, 9369319, 31988856, 54608393
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The lower principal and intermediate convergents to 2^(1/2), beginning with
1/1, 4/3, 7/5, 24/17, 41/29, form a strictly increasing sequence;
essentially, numerators=A143608 and denominators=A079496.
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REFERENCES
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Clark Kimberling, "Best lower and upper approximates to irrational numbers," Elemente der Mathematik, 52 (1997) 122-126.
Serge Lang, Introduction to Diophantine Approximations, Addison-Wesley, New York, 1966.
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LINKS
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Creighton Kenneth Dement, Comments on A143608 and A143609
C. Kimberling, Best lower and upper approximations to irrational numbers, Elem. Math. vol. 52 iss. 3 (1997) 122-126. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 08 2009]
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FORMULA
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Conjectures: a(n)=6*a(n-2)-a(n-4). G.f.: x*(1+4*x+x^2)/((x^2-2*x-1)*(x^2+2*x-1)). a(2n)=A005319(n). a(2n+1)=A002314(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 17 2009]
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CROSSREFS
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Sequence in context: A086968 A101824 A027946 this_sequence A079441 A129418 A073218
Adjacent sequences: A143605 A143606 A143607 this_sequence A143609 A143610 A143611
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Aug 27 2008
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