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Search: id:A080607
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| A080607 |
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Golomb's sequence using multiples of 3. |
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+0
4
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| 3, 3, 3, 6, 6, 6, 9, 9, 9, 12, 12, 12, 12, 12, 12, 15, 15, 15, 15, 15, 15, 18, 18, 18, 18, 18, 18, 21, 21, 21, 21, 21, 21, 21, 21, 21, 24, 24, 24, 24, 24, 24, 24, 24, 24, 27, 27, 27, 27, 27, 27, 27, 27, 27, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 33, 33, 33, 33, 33, 33
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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More generally let b(k) be a sequence of integers in arithmetic progression: b(k)=A*k+B, then the Golomb's sequence a(n) using b(k) is asymptotic to tau^(2-tau)*(A*n)^(tau-1).
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FORMULA
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a(n) is asymptotic to tau^(2-tau)*(3n)^(tau-1) and more precisely it seems that a(n)=round(tau^(2-tau)*(3n)^(tau-1)) +(-2, -1, +0, +1 or +1) where tau is the golden ratio.
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EXAMPLE
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Read 3,3,3,6,6,6,9,9,9,12,12,12,12,12,12,15 as (3,3,3),(6,6,6),(9,9,9),(12,12,12,12,12,12),... count occurrences between 2 parentheses, gives 3,3,3,6,... which is the sequence itself.
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CROSSREFS
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Cf. A001462 A080606, A080605.
Sequence in context: A108581 A073080 A057944 this_sequence A013322 A166273 A058675
Adjacent sequences: A080604 A080605 A080606 this_sequence A080608 A080609 A080610
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 25 2003
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