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Search: id:A005614
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| A005614 |
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Infinite Fibonacci word (start with 1, apply 0->1, 1->10, iterate). |
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+0
34
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| 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Characteristic function of A022342 . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), May 03 2004
a(n)=number of 0's between successive 1's (see also A003589 and A007538) - Eric Angelini (eric.angelini(AT)kntv.be), Jul 06 2005
With offset 1 this is the characteristic sequence for Wythoff A-numbers A000201=[1,3,4,6,...].
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REFERENCES
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F. Axel et al., Vibrational modes in a one dimensional "quasi-alloy": the Morse case, J. de Physique, Colloq. C3, Supp. to No. 7, Vol. 47 (Jul 1986), pp. C3-181-C3-186; see Eq. (10).
M. Bunder and K. Tognetti, On the self matching properties of [j tau], Discrete Math., 241 (2001), 139-151.
S. Dulucq and D. Gouyou-Beauchamps, Sur les facteurs des suites de Sturm, Theoret. Comput. Sci. 71 (1990), 381-400.
M. S. El Naschie, Statistical geometry of a Cantor discretum and semiconductors, Computers Math. Applic., 29 (No, 12, 1995), 103-110.
J. Grytczuk, Infinite semi-similar words, Discrete Math. 161 (1996), 133-141.
G. Melancon, Factorizing infinite words using Maple, MapleTech journal, vol. 4, no. 1, 1997, pp. 34-42, esp. p. 36.
G. Melancon, Lyndon factorization of sturmian words, Discr. Math., 210 (2000), 137-149.
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LINKS
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Joerg Arndt, Fxtbook
R. Knott, The Fibonacci Rabbit Sequence
J. O. Shallit, Characteristic words as fixed points of homomorphisms
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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Define strings S(0)=1, S(1)=10, S(n)=S(n-1)S(n-2); iterate.
floor((n+1)*u)-floor(n*u), u = (1-sqrt(5))/2.
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EXAMPLE
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The infinite word is 101101011011010110101101101011...
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MAPLE
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Digits := 50; u := evalf((1-sqrt(5))/2); A005614 := n->floor((n+1)*u)-floor(n*u);
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MATHEMATICA
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Nest[ Function[l, {Flatten[(l /. {0 -> {1}, 1 -> {1, 0}})]}], {1}, 10] (from Robert G. Wilson v Jan 30, 2005)
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PROGRAM
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(PARI) a(n, w1, s0, s1)=local(w2); for(i=2, n, w2=[ ]; for(k=1, length(w1), w2=concat(w2, if(w1[ k ], s1, s0))); w1=w2); w2
(PARI) for(n=2, 10, print(n" "a(n, [ 0 ], [ 1 ], [ 1, 0 ]))) \\ Gives successive convergents to sequence
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CROSSREFS
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Binary complement of A003849, which is the standard form of this sequence. Cf. A036299, A001468, A014675.
Two other essentially identical sequences are A096270, A114986.
Adjacent sequences: A005611 A005612 A005613 this_sequence A005615 A005616 A005617
Sequence in context: A096055 A125144 A115198 this_sequence A071036 A057078 A127245
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas
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EXTENSIONS
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Corrected by Clark Kimberling (ck6(AT)evansville.edu), Oct 04 2000
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