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A069202
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A Collatz - Fibonacci mixture: a(1) = 1, a(2) = 2, a(n+2) = a(n+1)/2+a(n)/2 if a(n+1) and a(n) have the same parity, a(n+2) = a(n+1)+a(n) otherwise.
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3
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1, 2, 3, 5, 4, 9, 13, 11, 12, 23, 35, 29, 32, 61, 93, 77, 85, 81, 83, 82, 165, 247, 206, 453, 659, 556, 1215, 1771, 1493, 1632, 3125, 4757, 3941, 4349, 4145, 4247, 4196, 8443, 12639, 10541, 11590, 22131, 33721, 27926, 61647, 89573, 75610, 165183, 240793
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| A Collatz-Fibonacci mixture. Does this sequence diverge to infinity? [Yes! See Amleh et a;. - N. J. A. Sloane, Jun 17 2009]
Conjecture: More generally let a(1)=x a(2)=y be 2 distinct positive integers then for any x,y >0 lim n -> infinity ln(a(n))/n = 1/4
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REFERENCES
| A. M. Amleh et al., On some difference equations ..., J. Math. Anal. Appl., 223 (1998), 196-215. [From N. J. A. Sloane, Jun 17 2009]
J. Greene, The unboundedness of a family of difference equations ..., Fib. Q., 46/47 (2008/2009), 146-152.[From N. J. A. Sloane, Jun 17 2009]
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FORMULA
| a(n+2)=2*(a(n+1)+a(n))/(3+(-1)^(a(n+1)+a(n)))
It seems that a(n)*exp(-n/4) is bounded.
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EXAMPLE
| a(1)=1 and a(2)=2 have different parities hence a(3)=a(2)+a(1)=3
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CROSSREFS
| Cf. A151749.
Sequence in context: A081025 A124653 A085947 * A100932 A064360 A075158
Adjacent sequences: A069199 A069200 A069201 * A069203 A069204 A069205
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KEYWORD
| easy,nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 11 2002
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