

A060032


Fixed point of the morphism 1 > 121, 2 > 122, starting from 1.


4




OFFSET

0,2


COMMENTS

Previous name was: Ana sequence.
Let A(n), N(n) denote the number of 1's and the number of 2's in a(n). Then A(n) = (3^(k1) + 1)/2, N(n) = (3^(k1)  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 nonoverlapping closed intervals as there are letters in the nth 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.


REFERENCES

C. Pickover, Wonders of Numbers, Chap. 69 "An A?", Oxford University Press, NY, 2001, p. 167171.


LINKS

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



KEYWORD

nonn


AUTHOR



EXTENSIONS

More descriptive name from comment, Joerg Arndt, Jan 23 2024


STATUS

approved



