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Search: id:A087475
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| 4, 5, 8, 13, 20, 29, 40, 53, 68, 85, 104, 125, 148, 173, 200, 229, 260, 293, 328, 365, 404, 445, 488, 533, 580, 629, 680, 733, 788, 845, 904, 965, 1028, 1093, 1160, 1229, 1300, 1373, 1448, 1525, 1604, 1685, 1768, 1853, 1940, 2029, 2120, 2213, 2308, 2405, 2504
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Schroeder, p. 330, states "For positive n, these winding numbers are precisely those whose continued fraction expansion is periodic and has period length 1".
Sequence allows us to find X values of the equation: X^3 - 4*X^2 = Y^2. To find Y values: b(n)=n*(n^2 + 4). - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 06 2007
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REFERENCES
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Manfred R. Schroeder, "Fractals, Chaos, Power Laws"; W.H. Freeman & Co, 1991, p. 330-331.
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LINKS
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Eric Weisstein's World of Mathematics, Near-Square Prime
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FORMULA
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n^2 + 4 are discriminant terms in the formula for Positive Silver Mean Constants, defined as barover[n], = [sqrt (n^2 + 4) - n]/2. Such constants barover[n] = C, have the property: 1/C - C = n
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EXAMPLE
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a(2) = 8, discriminant of algebraic representation of barover[2] = [2,2,2,...] = sqrt 2 - 1 = .41421356...= [(sqrt 8) - 2]/2. a(3) = 13, discriminant of barover[3] = [3,3,3...] = .3027756... = [(sqrt 13) - 3]/2
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CROSSREFS
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Cf. A005563, A046092, A001082, A002378, A036666, A062717, A028347.
Adjacent sequences: A087472 A087473 A087474 this_sequence A087476 A087477 A087478
Sequence in context: A133940 A030978 A101948 this_sequence A019526 A050892 A072808
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoogroups.com), Sep 09 2003
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EXTENSIONS
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More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net), Sep 14 2003
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