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 A084642 A Jacobsthal ratio. 0
 1, 3, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) = floor(A001045(n+1)/A001045(n)). The Jacobsthal recurrence means that A001045(n+1)/A001045(n) = 1+2/(A001045(n)/A001045(n-1)). The sequence of these fractions alternates after the first terms values just above 2 and just below 2, because the mapping x -> 1+2/x is concave in the neighborhood of x=2, where x=2 is an attractor. As a consequence, this sequence here iterates like A040001 or A000034 after a few terms. - R. J. Mathar, Sep 17 2008 LINKS FORMULA a(n) = floor((2^(n+1)+(-1)^n)/(2^n - (-1)^n)). CROSSREFS Cf. A000034. Sequence in context: A256253 A288818 A276988 * A271418 A230500 A010281 Adjacent sequences:  A084639 A084640 A084641 * A084643 A084644 A084645 KEYWORD easy,nonn AUTHOR Paul Barry, Jun 08 2003 STATUS approved

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