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A123564
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The infinite Fibonacci word reencoded by writing successive non-overlapping pairs of bits as decimal numbers.
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0
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2, 3, 1, 1, 2, 3, 1, 1, 2, 2, 3, 1, 2, 2, 3, 1, 2, 2, 3, 1, 1, 2, 3, 1, 1, 2, 2, 3, 1, 2, 2, 3, 1, 2, 2, 3, 1, 1, 2, 3, 1, 1, 2, 3, 1, 1, 2, 2, 3, 1, 2, 2, 3, 1, 1, 2, 3, 1, 1, 2, 3, 1, 1, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The algorithm used here suggests multiple variations such as using more than 2 bits, allowing overlap of successive subwords, using other numbers for the encoding of subwords or using other binary sequences. (E.g. overlapping: a(n)=2*A005614(n)+A005614(n+1) )
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FORMULA
| f=(sqrt(5)-1)/2; m=2*n; a(n)=floor(m*f)-2*floor((m-1)*f)+floor((m+1)*f); OR Using a previously generated Fibonacci word = A005614 : a(n)=2*A005614(2n-1)+A005614(2n)
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EXAMPLE
| a(1)=2*1+0=2
a(2)=2*1+1=3
a(3)=2*0+1=1
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PROG
| f=(sqrt(5)-1)/2; m=2*n; a(n)=floor(m*f)-2*floor((m-1)*f)+floor((m+1)*f); OR Using a previously generated Fibonacci word = A005614 : a(n)=2*A005614(2n-1)+A005614(2n)
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CROSSREFS
| Cf. A005614.
Sequence in context: A102383 A070913 A114280 * A065882 A007884 A190593
Adjacent sequences: A123561 A123562 A123563 * A123565 A123566 A123567
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KEYWORD
| easy,nonn
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AUTHOR
| Alexandre E. Losev (alosev(AT)svr.igic.bas.bg), Nov 12 2006
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