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A233590
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Decimal expansion of the continued fraction c(1) +c(1)/(c(2) +c(2)/(c(3) +c(3)/(c(4) +c(4)/....))), where c(i)=2^(i-1).
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10
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1, 4, 0, 8, 6, 1, 5, 9, 7, 9, 7, 3, 5, 0, 0, 5, 2, 0, 5, 1, 3, 2, 3, 6, 2, 5, 9, 0, 2, 5, 5, 7, 9, 5, 2, 0, 9, 4, 8, 4, 5, 6, 3, 3, 7, 3, 6, 8, 6, 8, 8, 8, 3, 5, 3, 7, 0, 3, 9, 2, 7, 0, 2, 2, 3, 7, 9, 7, 5, 9, 9, 8
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OFFSET
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1,2
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COMMENTS
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For more details about this type of continued fraction, see A233588.
This one corresponds to the powers of two sequence.
Corresponds to the regular continued fraction [1,2,2,4,4,8,8,16,16,...]. - Jeffrey Shallit, Jun 14 2016
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LINKS
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FORMULA
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Equals 1+1/(2+2/(4+4/(8+8/(16+16/(32+...))))).
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EXAMPLE
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1.408615979735005205132362590255795209484563373686888353703927022...
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MATHEMATICA
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RealDigits[ Fold[(#2 + #2/#1) &, 1, Reverse@ (2^Range[0, 27])], 10, 111][[1]] (* Robert G. Wilson v, May 22 2014 *)
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PROG
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(PARI) See the link
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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