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OFFSET
| 0,2
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COMMENTS
| Let A(n), N(n) denote the number of 1's and the number of 2's in a(n). Then A(n) = (3^(k-1) + 1)/2, N(n) = (3^(k-1) - 1)/2. Hence lim_{n} A(n)/N(n) = 1.
In "Wonders of Numbers", Pickover considers a "fractal bar code" constructed from the Ana sequence. Start with a segment I of fixed length; at stage n, evenly subdivide I into as many non-overlapping closed intervals as there are letters in the n-th term of the Ana sequence; then shade the intervals corresponding to a's. It can be shown that a fractal set defined from this construction has fractal dimension = 1.
A fixed point of the morphism 1 -> 121, 2 -> 122, starting from a(1) = 1. See A060236. - from Robert G. Wilson v Mar 05 2005)
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REFERENCES
| C. Pickover, Wonders of Numbers, Chap. 69 "An A?", Oxford University Press, NY, 2001, p. 167-171.
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LINKS
| Pe, J., Ana's Golden Fractal
C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review
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FORMULA
| Begin with the letter "a". Generate next term by using the indefinite article as appropriate, e.g. "an a", then "an a, an n, an a" etc. Assign a=1, n=2.
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EXAMPLE
| a(2) = ana = 121, a(3) = ana ann ana = 121122121.
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MATHEMATICA
| f[n_] := FromDigits[ Nest[ Flatten[ # /. {1 -> {1, 2, 1}, 2 -> {1, 2, 2}}] &, {1}, n]]; Table[ f[n], {n, 0, 4}] (from Robert G. Wilson v Mar 05 2005)
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CROSSREFS
| Sequence in context: A077735 A068121 A013859 * A109643 A080826 A043646
Adjacent sequences: A060029 A060030 A060031 * A060033 A060034 A060035
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KEYWORD
| nonn
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AUTHOR
| Jason Earls (zevi_35711(AT)yahoo.com), Mar 17 2001
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EXTENSIONS
| Additional comments from Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Mar 11 2002
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