|
| |
|
|
A038568
|
|
Numerators in canonical bijection from positive integers to positive rationals.
|
|
6
| |
|
|
1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 4, 1, 5, 2, 5, 3, 5, 4, 5, 1, 6, 5, 6, 1, 7, 2, 7, 3, 7, 4, 7, 5, 7, 6, 7, 1, 8, 3, 8, 5, 8, 7, 8, 1, 9, 2, 9, 4, 9, 5, 9, 7, 9, 8, 9, 1, 10, 3, 10, 7, 10, 9, 10, 1, 11, 2, 11, 3, 11, 4, 11, 5, 11, 6, 11, 7, 11, 8, 11, 9, 11, 10, 11, 1, 12, 5, 12, 7, 12, 11, 12, 1, 13, 2
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| Even-indexed terms are positive integers in order, with m occurring phi(m) times. Preceding odd-indexed terms (except for missing initial 0) are the corresponding numbers <= m and relatively prime to m, in increasing order. The denominators are just this sequence shifted left. Thus each positive rational occurs exactly once as a ratio a(n)/a(n+1). - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Dec 06 2006
|
|
|
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 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).
|
|
|
MAPLE
| with (numtheory): A038568 := 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 (j-1) fi: RETURN (k-1): end: # from UlrSchimke(AT)aol.com, Oct 31, 2001
|
|
|
CROSSREFS
| Cf. A020652, A020653, A038566-A038569.
Sequence in context: A057940 A097285 A057432 * A071912 A070940 A020651
Adjacent sequences: A038565 A038566 A038567 * A038569 A038570 A038571
|
|
|
KEYWORD
| nonn,frac,core,easy,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
|
| |
|
|
