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Search: id:A140357
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| A140357 |
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a(1)=1; a(n)=floor(4*a(n-1)*(n-a(n-1) / n) for n > 1. |
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+0
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| 1, 2, 2, 4, 3, 6, 3, 7, 6, 9, 6, 12, 3, 9, 14, 7, 16, 7, 17, 10, 20, 7, 19, 15, 24, 7, 20, 22, 21, 25, 19, 30, 10, 28, 22, 34, 11, 31, 25, 37, 14, 37, 20, 43, 7, 23, 46, 7, 24, 49, 7, 24, 52, 7, 24, 54, 11, 35, 56, 14, 43, 52, 36, 63, 7, 25, 62, 21, 58, 39, 70, 7, 25, 66, 31, 73, 15, 48
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n)/n approximates the behavior of the logistic map x(n+1) = r*x(n)*(1-x(n)) at the critical value r = 4 where its iterated behavior becomes chaotic.
Conjecture: starting with any given n and any 1 <= a(n) <= n and applying the rule for the sequence produces a sequence which eventually joins this one. For example, starting with a(9)=5, the sequence continues 10,3,9,11,9, at which point it has joined.
There is a number x(1) such that iterating the logistic map x(n+1) = 4*x(n)*(1-x(n)) approaches a(n)/n; in particular x(n) > 1/2 iff a(n)/n > 1/2, and lim_{n->infinity} x(n)-a(n)/n = 0. x(1) is approximately 0.74300456748016924159182578873962328734252790178266693834898117732270042549583799064232908893034253248. It appears that |x(n)-a(n)/n| < 1/sqrt(n) for all n.
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LINKS
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Eric Weisstein's World of Mathematics, Logistic Map.
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CROSSREFS
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Cf. A079271, A087089, A098587, A118454.
Adjacent sequences: A140354 A140355 A140356 this_sequence A140358 A140359 A140360
Sequence in context: A126090 A058266 A138664 this_sequence A089265 A113885 A113886
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KEYWORD
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easy,nonn
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AUTHOR
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Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), May 30 2008, May 31 2008
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