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Search: id:A143643
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| A143643 |
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Lower principal and intermediate convergents to 3^(1/2). |
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+0
3
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| 1, 3, 5, 12, 19, 45, 71, 168, 265, 627, 989, 2340, 3691, 8733, 13775, 32592, 51409, 121635, 191861, 453948, 716035, 1694157, 2672279, 6322680, 9973081, 23596563
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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 3^(1/2), beginning with
1/1, 3/2, 5/3, 12/7, 19/11, form a strictly increasing sequence; essentially, numerators=A143643 and denominators=A005246.
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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: A082740 A010067 A024458 this_sequence A089292 A143360 A034763
Adjacent sequences: A143640 A143641 A143642 this_sequence A143644 A143645 A143646
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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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