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Search: id:A053518
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| A053518 |
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Numerators of successive convergents to continued fraction 1+2/(3+3/(4+4/(5+5/(6+6/(7+7/(8+8/(9+9/10+...))))))). |
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+0
5
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| 1, 5, 23, 45, 925, 7285, 7195, 641075, 6993545, 27779915, 1077005935, 15001154095, 6788401045, 3570274674605, 60484653310955, 40198648188145, 1869525647793155, 31559031031400605, 2865359642850975565
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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A053518/A053519 -> (2*e-5)/(3-e) = 1.5496467783... as n-> infinity.
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REFERENCES
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L. Lorentzen and H. Waadeland, Continued Fractions with Applications, North-Holland 1992, p. 562.
E. Maor, e: The Story of a Number, Princeton Univ. Press 1994, pp. 151 and 157.
M. A. Stern, Theorie der Kettenbr"uche und ihre Anwendung, Crelle, 1832, pp. 1-22.
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LINKS
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Leonhardo Eulero, Introductio in analysin infinitorum. Tomus primus, Lausanne, 1748.
L. Euler, Introduction a l'analyse infinitesimal Tome premier, Tome second, trad. du latin en francais par J. B. Labey, Paris, 1796-1797.
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EXAMPLE
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Convergents are 1, 5/3, 23/15, 45/29, 925/597, 7285/4701, ...
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MAPLE
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for j from 1 to 50 do printf(`%d, `, numer(cfrac([1, seq([i, i+1], i=2..j)]))); od:
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CROSSREFS
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Cf. A053519, A053520, A053556, A053557.
Sequence in context: A062341 A121308 A146467 this_sequence A154625 A107011 A031387
Adjacent sequences: A053515 A053516 A053517 this_sequence A053519 A053520 A053521
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KEYWORD
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nonn,frac,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jan 15 2000
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EXTENSIONS
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Thanks to R. K. Guy, S. R. Finch, R. W. Gosper for comments.
More terms from James A. Sellers (sellersj(AT)math.psu.edu), Feb 02 2000
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