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Search: id:A069202
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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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+0
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; listen)
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OFFSET
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1,2
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COMMENT
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A Collatz-Fibonacci mixture. Does this sequence diverge to infinity?
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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FORMULA
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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
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a(1)=1 and a(2)=2 have different parities hence a(3)=a(2)+a(1)=3
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CROSSREFS
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Adjacent sequences: A069199 A069200 A069201 this_sequence A069203 A069204 A069205
Sequence in context: A081025 A124653 A085947 this_sequence A100932 A064360 A075158
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 11 2002
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