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Search: id:A143609
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| A143609 |
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Numerators of the upper principal and intermediate convergents to 2^(1/2). |
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4
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| 2, 3, 10, 17, 58, 99, 338, 577, 1970, 3363, 11482, 19601, 66922, 114243, 390050, 665857, 2273378, 3880899, 13250218, 22619537, 77227930
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OFFSET
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1,1
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COMMENT
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The upper principal and intermediate convergents to 2^(1/2), beginning with
2/1, 3/2, 10/7, 17/12, 58/41, form a strictly decreasing sequence;
essentially, numerators=A143609 and denominators=A084068.
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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
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CROSSREFS
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Sequence in context: A135061 A069156 A060744 this_sequence A066915 A070253 A147673
Adjacent sequences: A143606 A143607 A143608 this_sequence A143610 A143611 A143612
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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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