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A038569
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Denominators in canonical bijection from positive integers to positive rationals.
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10
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1, 2, 1, 3, 1, 3, 2, 4, 1, 4, 3, 5, 1, 5, 2, 5, 3, 5, 4, 6, 1, 6, 5, 7, 1, 7, 2, 7, 3, 7, 4, 7, 5, 7, 6, 8, 1, 8, 3, 8, 5, 8, 7, 9, 1, 9, 2, 9, 4, 9, 5, 9, 7, 9, 8, 10, 1, 10, 3, 10, 7, 10, 9, 11, 1, 11, 2, 11, 3, 11, 4, 11, 5, 11, 6, 11, 7, 11, 8, 11, 9, 11, 10, 12, 1, 12, 5, 12, 7, 12, 11, 13, 1, 13
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OFFSET
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0,2
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REFERENCES
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H. Lauwerier, Fractals, Princeton Univ. Press, p. 23.
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LINKS
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David Wasserman, Table of n, a(n) for n = 0..100000
Index entries for "core" sequences
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EXAMPLE
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First arrange fractions by increasing denominator then by increasing numerator:
1/1, 1/2, 1/3, 2/3, 1/4, 3/4, 1/5, 2/5, 3/5, ... (this is A038566/A038567);
now follow each term by its reciprocal:
1/1, 1/2, 2/1, 1/3, 3/1, 2/3, 3/2, 1/4, 4/1, 3/4, 4/3, ... (this is A038568/A038569).
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MAPLE
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with (numtheory): A038569 := proc (n) local sum, j, k; sum := 1: k := 2: while (sum < n) do: sum := sum + 2 * phi(k): k := k + 1: od: sum := sum - 2 * phi(k-1): j := 1: while sum < n do: if gcd(j, k-1) = 1 then sum := sum + 2: fi: j := j+1: od: if sum > n then RETURN (k-1) fi: RETURN (j-1): end: # from UlrSchimke(AT)aol.com, Oct 31, 2001
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MATHEMATICA
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a[n_] := Module[{s = 1, k = 2, j = 1}, While[s <= n, s = s + 2*EulerPhi[k]; k = k+1]; s = s - 2*EulerPhi[k-1]; While[s <= n, If[GCD[j, k-1] == 1, s = s+2]; j = j+1]; If[s > n+1, k-1, j-1]]; Table[a[n], {n, 0, 99}](* From Jean-François Alcover, Nov 10 2011, after Maple *)
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CROSSREFS
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Cf. A020652, A020653, A038566-A038569.
Sequence in context: A025808 A144079 A071575 * A020650 A124224 A014599
Adjacent sequences: A038566 A038567 A038568 * A038570 A038571 A038572
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KEYWORD
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nonn,frac,core,nice
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Erich Friedman.
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STATUS
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approved
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