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 A014675 The infinite Fibonacci word (start with 1, apply 1->2, 2->21, take limit). 34
 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The limiting mean and variance of the first n terms are both equal to the golden ratio (A001622). - Clark Kimberling, Mar 12 2014 Let F = A000045 (Fibonacci numbers).  For n >= 3, the first F(n)-2 terms of A014675 form a palindrome; see A001911.  If k is not one of the numbers F(n)-2, then the first k terms of A014675 do not form a palindrome. - Clark Kimberling, Jul 14 2014 First differences of A000201. - Tom Edgar, Apr 23 2015 [Editor's note: except for the offset: as for A022342, below. - M. F. Hasler, Oct 13 2017] Also first differences of A022342 (which starts at offset 1): a(n)=A022342(n+2)-A022342(n+1), n >= 0. Equal to A001468 without its first term: a(n) = A001468(n+1), n >= 0. - M. F. Hasler, Oct 13 2017 REFERENCES D. Gault and M. Clint, "Curiouser and curiouser" said Alice. Further reflections on an interesting recursive function, Internat. J. Computer Math., 26 (1988), 35-43. See Table 2. D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7, p. 36. G. Melancon, Factorizing infinite words using Maple, MapleTech journal, vol. 4, no. 1, 1997, pp. 34-42, esp. p. 36. LINKS T. D. Noe, Table of n, a(n) for n = 0..10945 (20 iterations) M. Bunder and K. Tognetti, On the self matching properties of [j tau], Discrete Math., 241 (2001), 139-151. D. Gault & M. Clint, "Curiouser and curiouser said Alice. Further reflections on an interesting recursive function, Intern. J. Computer. Math., 26 (1988), 35-43. (Annotated scanned copy) J. Grytczuk, Infinite semi-similar words, Discrete Math. 161 (1996), 133-141. G. Melancon, Lyndon factorization of sturmian words, Discr. Math., 210 (2000), 137-149. FORMULA Define strings S(0)=1, S(1)=2, S(n)=S(n-1).S(n-2) for n>=2. Sequence is S(infinity). a(n) = floor((n+2)*phi) - floor((n+1)*phi) = A000201(n+2) - A000201(n+1), phi = (1 + sqrt(5))/2. MAPLE Digits := 50: t := evalf( (1+sqrt(5))/2); A014675 := n->floor((n+2)*t)-floor((n+1)*t); MATHEMATICA Nest[ Flatten[ # /. {1 -> 2, 2 -> {2, 1}}] &, {1}, 11] (* Robert G. Wilson v *) PROG (PARI) first(n)=my(v=, u); while(#v

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Last modified July 11 14:30 EDT 2020. Contains 335626 sequences. (Running on oeis4.)