OFFSET
1,2
COMMENTS
A "non-commutative Fibonacci" sequence. Often written as: a, b, ba, bab, babba, babbabab, babbababbabba, babbababbabbababbabab, ...
Converges in the appropriate topology. - Dylan Thurston, Jan 28 2005
Do a web search on babbababbabbababbabab to get further links.
a(n) has Fibonacci(n) digits d_i where 1 <= i <= n and n > 2. If i is in A001950 then d_i = 1, otherwise it is 2 [Stolarsky]. - David A. Corneth, May 14 2017
REFERENCES
D. E. Knuth, "The Art of Programming", Volume 1, "Fundamental Algorithms", third edition, problem 36 on page 86.
LINKS
K. B. Stolarsky, Beatty sequences, continued fractions, and certain shift operators, Canadian Math. Bull. 19 (1976) pp. 473-482.
Wikipedia, Lindenmayer system
MATHEMATICA
a[1] = 1; a[2] = 2; a[n_] := 10^Floor[ Log[10, a[n - 2]] +1]*a[n - 1] + a[n - 2] (* Robert G. Wilson v, Jan 26 2006 *)
PROG
(PARI) a(n) = if (n<=2, n, eval(concat(Str(a(n-1)), Str(a(n-2))))); \\ Michel Marcus, May 14 2017
(PARI) a(n) = {if(n<=2, return(n));
my(v=vector(fibonacci(n), i, 2), phi2 = (3+sqrt(5))/2, b = vector(fibonacci(n-2), i, (i*(sqrt(5)+3)/2))\1); for(i=1, fibonacci(n-2), v[(i*(3+sqrt(5))/2)\1] = 1); sum(i=1, #v, 10^(#v-i) * v[i])}
a(n) = my(v=vector(n)); if(n <= 2, return(n)); v[1] = 1; v[2] = 2; for(i=3, n, v[i]=eval(concat(Str(v[i-1]), Str(v[i-2])))); v[#v] \\ David A. Corneth, May 14 2017
CROSSREFS
KEYWORD
nonn,base
AUTHOR
EXTENSIONS
Title clarified by Chai Wah Wu, Mar 17 2021
STATUS
approved