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Search: id:A127614
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| A127614 |
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a(n) = numerator of the continued fraction which has the positive integers which are <= n and are coprime to n as its terms. |
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+0
3
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| 1, 1, 3, 4, 43, 6, 1393, 151, 3980, 265, 7489051, 479, 1004933203, 28065, 1567857, 3025576, 44811373131073, 107069, 13807296146243251, 12541924, 85867066404, 1867630045, 2448516766522879398193, 47040432, 85536466996746340043
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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The positive integers coprime to n and <= n can be written either from largest to smallest or from smallest to largest, and the numerator of the continued fraction would remain unchanged.
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EXAMPLE
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The positive integers coprime to 8 and <= 8 are 1,3,5,7. So a(8) is the numerator of 1 +1/(3 +1/(5 +1/7)) = 151/115. a(8) is also the numerator of 7 +1/(5 +1/(3 +1/1)) = 151/21.
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MATHEMATICA
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f[n_] := Select[Range[n], GCD[ #, n] == 1 &]; g[n_] := Numerator[FromContinuedFraction[f[n]]]; Table[g[n], {n, 26}] (*Chandler*)
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CROSSREFS
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Cf. A127615, A127616.
Sequence in context: A012472 A012876 A032837 this_sequence A041055 A032838 A013336
Adjacent sequences: A127611 A127612 A127613 this_sequence A127615 A127616 A127617
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KEYWORD
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frac,nonn
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), Jan 19 2007
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Jan 22 2007
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