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A020653 Denominators in canonical bijection from positive integers to positive rationals. 19
1, 2, 1, 3, 1, 4, 3, 2, 1, 5, 1, 6, 5, 4, 3, 2, 1, 7, 5, 3, 1, 8, 7, 5, 4, 2, 1, 9, 7, 3, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 11, 7, 5, 1, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 13, 11, 9, 5, 3, 1, 14, 13, 11, 8, 7, 4, 2, 1, 15, 13, 11, 9, 7, 5, 3, 1, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 17 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

Richard Courant and Herbert Robbins. What Is Mathematics?, Oxford, 1941, pp. 79-80.

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

LINKS

David Wasserman, Table of n, a(n) for n = 1..100000

Index entries for "core" sequences

MAPLE

with (numtheory): A020653 := 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 (k-j): end: # Ulrich Schimke (ulrschimke(AT)aol.com), Nov 06 2001

MATHEMATICA

a[n_] := Module[{s=0, k=2}, While [s < n, s = s + EulerPhi[k]; k = k+1]; s = s - EulerPhi[k-1]; j=1; While[s < n , If[GCD[j, k-1] == 1 , s = s+1]; j = j+1]; k-j]; Table[a[n], {n, 1, 96}] (* Jean-Fran├žois Alcover, Dec 06 2012, after Ulrich Schimke's Maple program *)

Flatten[Map[Denominator[#/Reverse[#]]&, Table[Flatten[Position[GCD[Map[Mod[#, n]&, Range[n-1]], n], 1]], {n, 100}]]] (* Peter J. C. Moses, Apr 17 2013 *)

PROG

(Haskell)

a020653 n = a020653_list !! (n-1)

a020653_list = concat $ map reverse $ tail a038566_tabf

-- Reinhard Zumkeller, Oct 30 2012

(Python)

from sympy import totient, gcd

def a(n):

    s=0

    k=2

    while s<n:

        s+=totient(k)

        k+=1

    s-=totient(k - 1)

    j=1

    while s<n:

        if gcd(j, k - 1)==1: s+=1

        j+=1

    return k - j # Indranil Ghosh, May 23 2017, translated from Ulrich Schimke's MAPLE code

CROSSREFS

Cf. A020652, A038566.

Sequence in context: A088445 A280696 A293247 * A094522 A233204 A118487

Adjacent sequences:  A020650 A020651 A020652 * A020654 A020655 A020656

KEYWORD

nonn,frac,core,nice

AUTHOR

David W. Wilson

STATUS

approved

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Last modified January 20 17:37 EST 2018. Contains 297961 sequences.