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Search: id:A137595
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| A137595 |
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Decimal-binary representations of palindromic continued fractions. |
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+0
1
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| 1, 3, 6, 7, 13, 15, 25, 26, 28, 31, 49, 53, 59, 63
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Using the conversion rules, the first 14 fractions in the Stern-Brocot infinite Farey tree, (rational fractions k, 0<k<1) with palindromic continued fraction representations are: 1/2, 1/3, 2/5, 1/4, 3/8, 1/5, 5/12, 5/13, 3/10, 1/6, 7/16, 8/21, 4/15, 1/7.
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FORMULA
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Binary terms such that duplicating the rightmost bit gives a palindrome when counting repeated bits.
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EXAMPLE
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The first 14 binary terms corresponding to (1, 3, 6, 7,...) = 1, 11, 110, 111, 1101, 1111, 1101, 11010, 11100, 11111, 110001, 110101, 111011, 111111,...).
Appending a duplicate of the rightmost bit to each of the terms, then recording the number of repeats gives an palindrome.
Example: 26 = 11010. Appending an 0 to the right gives 110100. Recording the number of repeats, we get 2112, a palindrome. Last, we obtain the fraction corresponding to continued fraction 2112 = 5/13.
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CROSSREFS
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Adjacent sequences: A137592 A137593 A137594 this_sequence A137596 A137597 A137598
Sequence in context: A047705 A069891 A088146 this_sequence A033053 A107850 A051218
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 29 2008
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