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Search: id:A001468
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| A001468 |
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There are a(n) 2's between successive 1's.
(Formerly M0099 N0036)
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+0
12
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| 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, 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
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Another version of the infinite Fibonacci word. See A003849 for the standard form.
Start with 1, apply 1->12, 2->122, take limit . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 23 2005
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REFERENCES
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M. Bunder and K. Tognetti, On the self matching properties of [j tau], Discrete Math., 241 (2001), 139-151.
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.
D. R. Hofstadter, personal communication.
Problem E1226, Amer. Math. Monthly, 64 (1957), 197-198.
Problem 4247, Amer. Math. Monthly, 55 (1948), 588-592.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
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[(n+1) tau] - [n tau], tau =(1 + sqrt 5)/2 = A001622, [] = floor function.
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MAPLE
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Digits := 50: t := evalf( (1+sqrt(5))/2); A001468 := n->floor((n+1)*t)-floor(n*t);
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MATHEMATICA
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Table[Floor[GoldenRatio*(n + 1)] - Floor[GoldenRatio*n], {n, 0, 80}] - Joseph Biberstine (jrbibers(AT)indiana.edu), Aug 14 2006
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CROSSREFS
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Same as A014675 if initial 1 is deleted. Cf. A003849.
Sequence in context: A025143 A080634 A109925 this_sequence A014675 A107362 A166332
Adjacent sequences: A001465 A001466 A001467 this_sequence A001469 A001470 A001471
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com). Rechecked Nov 07, 2001
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