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A020652
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Numerators in canonical bijection from positive integers to positive rationals.
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22
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1, 1, 2, 1, 3, 1, 2, 3, 4, 1, 5, 1, 2, 3, 4, 5, 6, 1, 3, 5, 7, 1, 2, 4, 5, 7, 8, 1, 3, 7, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 5, 7, 11, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 3, 5, 9, 11, 13, 1, 2, 4, 7, 8, 11, 13, 14, 1, 3, 5, 7, 9, 11, 13, 15, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1, 5
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OFFSET
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1,3
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COMMENTS
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a(A002088(n)) = 1 for n > 1. - Reinhard Zumkeller, Jul 29 2012
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REFERENCES
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S. Cook, Problem 511: An Enumeration Problem, Journal of Recreational Mathematics, Vol. 9:2 (1976-77), 137. Solution by the Problem Editor, JRM, Vol. 10:2 (1977-78), 122-123.
Richard Courant and Herbert Robbins. What Is Mathematics?, Oxford, 1941, pp. 79-80.
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 = 1..100000
Paul Yiu, Recreational Mathematics, 24.3.1 Appendix: Two enumerations of the rational numbers in (0,1), page 633.
Index entries for sequences related to Stern's sequences
Index entries for "core" sequences
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EXAMPLE
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Arrange positive fractions < 1 by increasing denominator then by increasing numerator: 1/2, 1/3, 2/3, 1/4, 3/4, 1/5, 2/5, 3/5, 4/5, 1/6 ... (this is A020652/A038567). [From William Rex Marshall, Dec 16 2010]
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MAPLE
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with (numtheory): A020652 := proc (n) local sum, j, k; sum := 0: k := 2: while (sum < n) do: sum := sum + phi(k): k := k + 1: od: sum := sum - phi(k-1): j := 1; while sum < n do: if gcd(j, k-1) = 1 then sum := sum + 1: fi: j := j+1: od: RETURN (j-1): end: # from UlrSchimke(AT)aol.com, Nov 06, 2001
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MATHEMATICA
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Reap[Do[If[GCD[num, den] == 1, Sow[num]], {den, 1, 20}, {num, 1, den-1}] ][[2, 1]] (* Jean-François Alcover, Oct 22 2012 *)
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PROG
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(Haskell)
a020652 n = a020652_list !! (n-1)
a020652_list = map fst [(u, v) | v <- [1..], u <- [1..v-1], gcd u v == 1]
-- Reinhard Zumkeller, Jul 29 2012
(PARI) a(n)=my(s, j=1, k=1); while(s<n, s+=eulerphi(k++); ); s-=eulerphi(k); while(s<n, if(gcd(j, k)==1, s++); j++); j-1 \\ Charles R Greathouse IV, Feb 07 2013
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CROSSREFS
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Essentially the same as A038566, which is the main entry for this sequence.
Cf. A020653, A038567-A038569, A182972-A182976.
A054424 gives mapping to Stern-Brocot tree.
Cf. A037161.
Sequence in context: A132589 A054843 A038566 * A096107 A128487 A056609
Adjacent sequences: A020649 A020650 A020651 * A020653 A020654 A020655
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KEYWORD
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nonn,frac,core,nice
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AUTHOR
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David W. Wilson
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STATUS
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approved
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