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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: A025808 A144079 A071575 * A020650 A124224 A290089

Adjacent sequences:  A038566 A038567 A038568 * A038570 A038571 A038572

KEYWORD

nonn,frac,core,nice,changed

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Erich Friedman

STATUS

approved

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Last modified January 18 20:19 EST 2018. Contains 297865 sequences.