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Search: id:A143642
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| A143642 |
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Numerators of principal and intermediate convergents to 3^(1/2). |
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3
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| 1, 2, 3, 5, 7, 12, 19, 26, 45, 71, 97, 168, 265, 362, 627, 989, 1351, 2340, 3691, 5042, 8733, 13775, 18817, 32592, 51409, 70226, 121635, 191861, 262087, 453948, 716035, 978122, 1694157, 2672279, 3650401, 6322680, 9973081, 13623482, 23596563
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OFFSET
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1,2
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COMMENT
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The first few principal and intermediate convergents to 3^(1/2) are
1/1, 2/1, 3/2, 5/3, 7/4, 12/7; essentially, numerators=A143642 and
denominators=A140827.
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REFERENCES
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Serge Lang, Introduction to Diophantine Approximations, Addison-Wesley, New York, 1966.
Clark Kimberling, "Best lower and upper approximates to irrational numbers," Elemente der Mathematik, 52 (1997) 122-126.
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CROSSREFS
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Sequence in context: A091696 A048808 A013983 this_sequence A060986 A054540 A117537
Adjacent sequences: A143639 A143640 A143641 this_sequence A143643 A143644 A143645
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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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