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Search: id:A073116
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| A073116 |
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Continued fraction expansion of S/2 where S = sum( k>=0,1/2^floor(k*PHI) ) and PHI is the golden ratio (1+sqrt(5))/2. |
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+0
1
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| 0, 1, 5, 1, 8, 4, 64, 128, 16384, 1048576, 34359738368, 18014398509481984, 1237940039285380274899124224
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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The number S is the number whose digits are obtained from the substitution system (1->(1,0),0->(1)). The n-th term of the continued fraction expansion for S is 2^Fibonacci(n-2) ) (cf. A000301). This number S is known to be transcendental. The continued fraction of S/2^m follows the same kind of rule as for S/2.
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FORMULA
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If n>2 a(2n+1)=2^(F(2n-1)+1) a(2n)= 2^(F(2n-2)-1) where F(n) is the n-th Fibonacci number
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CROSSREFS
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Sequence in context: A006569 A126155 A021197 this_sequence A154310 A115521 A140705
Adjacent sequences: A073113 A073114 A073115 this_sequence A073117 A073118 A073119
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KEYWORD
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base,cofr,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 19 2002
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