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A061107
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In the Fibonacci rabbit problem we start with an immature pair 'I' which matures after one season to 'M'. This mature pair after one season stays alive and breeds a new immature pair and we get the following sequence I, MI, MIM, MIMMI, MIMMIMIM, MIMMIMIMMIMMI... if we replace 'I' by a '0' and 'M' by a '1' we get the required binary sequence.
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5
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0, 1, 10, 101, 10110, 10110101, 1011010110110, 101101011011010110101, 1011010110110101101011011010110110, 1011010110110101101011011010110110101101011011010110101
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| Amarnath Murthy, Smarandache Reverse auto correlated sequences and some Fibonacci derived sequences, Smarandache Notions Journal Vol. 12, No. 1-2-3, Spring 2001.
Ian Stewart, The Magical Maze.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,15
M. L. Perez et al., eds., Smarandache Notions Journal
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FORMULA
| a(1) = 0, a(2) =1, a(n) =concatenation of a(n-1) and a(n-2).
a(n)=a(n-1)*2^floor(log_2(a(n-2))+1)+a(n-2), for n>2, a(2)=10 (base 2). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 26 2007
a(n)=A036299(n-1), n>0. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 02 2008]
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EXAMPLE
| a(1) = 0, a(2) = 1, a(3) = a(2)a(1)= 10, etc.
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PROG
| (PARI) { default(realprecision, 100); L=log(10); for (n=0, 15, if (n>2, a=a1*10^(log(a2)\L + 1) + a2; a2=a1; a1=a, if (n==0, a=0, if (n==1, a=a2=1, a=a1=10))); write("b061107.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 18 2009]
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CROSSREFS
| Cf. A063896, A131242. See A005203 for the sequence version converted to decimal.
Sequence in context: A162849 A041182 * A036299 A015498 A039393 A203569
Adjacent sequences: A061104 A061105 A061106 * A061108 A061109 A061110
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KEYWORD
| base,nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 20 2001
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EXTENSIONS
| More terms from Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 26 2007
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