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 A230603 Generalized Fibonacci word. Binary complement of A221150. 2
 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0 COMMENTS Define strings S(0) = 1, S(1)= 110, thereafter S(n) = S(n-1)S(n-2); this sequence is the limit string S(infinity). See the examples below. LINKS FORMULA a(n) = floor((n + 2)/(3 - phi)) - floor((n + 1)/(3 - phi)), where phi = 1/2*(1 + sqrt(5)) is the golden ratio. If we read the sequence as the decimal constant C = 0.11011 10110 11101 11011 01110 ... then C = sum {n >= 1} 1/10^floor(n*(3 - phi)). 9*C has the simple continued fraction expansion [0; 1, 110, 10^1, 10^3, 10^4, 10^7, ..., 10^Lucas(n), ...]. EXAMPLE S(0) = 1 S(1) = 110 S(2) = 110 1 S(3) = 1101 110 S(4) = 1101110 1101 S(5) = 11011101101 1101110 The sequence of word lengths [1, 2, 4, 7, 11, 18, ...] is A000204. MAPLE Digits := 50: u := evalf((5-sqrt(5))/2): A230603 := n->floor((n+2)/u)-floor((n+1)/u): seq(A230603(n), n = 0..80); CROSSREFS Cf. A000204, A003849, A005614, A221150. Sequence in context: A188090 A004547 A285358 * A229343 A085369 A188082 Adjacent sequences:  A230600 A230601 A230602 * A230604 A230605 A230606 KEYWORD nonn,easy AUTHOR Peter Bala, Nov 22 2013 STATUS approved

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Last modified May 24 10:48 EDT 2019. Contains 323529 sequences. (Running on oeis4.)