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A038569 Denominators in canonical bijection from positive integers to positive rationals. 10
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

H. Lauwerier, Fractals, Princeton Univ. Press, p. 23.

LINKS

David Wasserman, Table of n, a(n) for n = 0..100000

Index entries for "core" sequences

EXAMPLE

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 with 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).

MAPLE

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: # Ulrich Schimke (ulrschimke(AT)aol.com)

MATHEMATICA

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}](* Jean-Fran├žois Alcover, Nov 10 2011, after Maple *)

PROG

(Python)

from sympy import totient, gcd

def a(n):

    s=1

    k=2

    while s<=n:

        s+=2*totient(k)

        k+=1

    s-=2*totient(k - 1)

    j=1

    while s<=n:

        if gcd(j, k - 1)==1: s+=2

        j+=1

    if s>n + 1: return k - 1

    return j - 1 # Indranil Ghosh, May 23 2017, translated from Mathematica

CROSSREFS

Cf. A020652, A020653, A038566-A038569.

Sequence in context: A307908 A316436 A303674 * A308686 A020650 A124224

Adjacent sequences:  A038566 A038567 A038568 * A038570 A038571 A038572

KEYWORD

nonn,frac,core,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Erich Friedman

STATUS

approved

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Last modified February 16 15:55 EST 2020. Contains 331961 sequences. (Running on oeis4.)