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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

Table of n, a(n) for n=0..104.

FORMULA

a(n) = floor((2^(n+1)+(-1)^n)/(2^n - (-1)^n)).

CROSSREFS

Cf. A000034.

Sequence in context: A212305 A205555 A165913 * A230500 A010281 A080131

Adjacent sequences:  A084639 A084640 A084641 * A084643 A084644 A084645

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jun 08 2003

STATUS

approved

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Last modified December 21 20:27 EST 2014. Contains 252326 sequences.