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Search: id:A013648
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| A013648 |
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Numbers n such that period of continued fraction for sqrt(n) contains a single 1. |
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+0
3
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| 3, 8, 15, 24, 35, 48, 63, 80, 99, 120, 143, 168, 175, 176, 195, 208, 224, 255, 288, 323, 360, 399, 440, 483, 528, 551, 575, 624, 675, 728, 783, 799, 840, 899, 960, 1023, 1035, 1088, 1155, 1224, 1247, 1295, 1368, 1403, 1443, 1520, 1599, 1680, 1763, 1848, 1872
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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All terms listed have continued fraction for sqrt(n^2+2n) of the form n, 1, 2n, 1, 2n, 1, 2n, etc. So all the terms of A005563 are here, as well as some additional terms (with even period > 2 and the digit 1 in central position) (e.g. sqrt(175)=[13,'4, 2, 1, 2, 4, 26']).
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REFERENCES
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Kenneth H. Rosen, Elementary Number Theory and Its Applications, Addison-Wesley, 1984, page 426 (but beware of errors!).
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LINKS
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R. Macmillan, Continued fractions, Math. Gaz. 84, 2000. See p. 34.
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FORMULA
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Are the numbers C(n+1, 1)*C(n+3, 1)? - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 02 2005
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MAPLE
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seq(2*(n+1)*binomial(n, 2)/n, n=2..45); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 28 2007
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CROSSREFS
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Cf. A040001, A040005, A040011, A040019, A040029, etc.
Union of A005563 and A102538.
Cf. A062196.
Adjacent sequences: A013645 A013646 A013647 this_sequence A013649 A013650 A013651
Sequence in context: A064356 A086959 A083656 this_sequence A005563 A132411 A067998
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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)
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EXTENSIONS
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Additional comments from Francisco Salinas (franciscodesalinas(AT)hotmail.com), Dec 30 2001
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