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A060032 Ana sequence. 3
1, 121, 121122121, 121122121121122122121122121, 121122121121122122121122121121122121121122122121122122121122121121122122121122121 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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. - Robert G. Wilson v, Mar 05 2005

REFERENCES

C. Pickover, Wonders of Numbers, Chap. 69 "An A?", Oxford University Press, NY, 2001, p. 167-171.

LINKS

Table of n, a(n) for n=0..4.

Pe, J., Ana's Golden Fractal

C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review

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.

EXAMPLE

a(2) = ana = 121, a(3) = ana ann ana = 121122121.

MATHEMATICA

f[n_] := FromDigits[ Nest[ Flatten[ # /. {1 -> {1, 2, 1}, 2 -> {1, 2, 2}}] &, {1}, n]]; Table[ f[n], {n, 0, 4}] (* Robert G. Wilson v, Mar 05 2005 *)

CROSSREFS

Sequence in context: A068121 A013859 A303897 * A109643 A080826 A043646

Adjacent sequences:  A060029 A060030 A060031 * A060033 A060034 A060035

KEYWORD

nonn

AUTHOR

Jason Earls, Mar 17 2001

EXTENSIONS

Additional comments from Joseph L. Pe, Mar 11 2002

STATUS

approved

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Last modified November 19 05:29 EST 2018. Contains 317333 sequences. (Running on oeis4.)