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Search: id:A038567
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| A038567 |
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Denominators in canonical bijection from positive integers to positive rationals <= 1. |
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+0
11
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| 1, 2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Least k such that phi(1)+phi(2)+phi(3)+...+phi(k) >= n - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 17 2002
Sum of numerator and denominator of fractions arranged by Cantor's ordering (1/1, 2/1, 1/2, 1/3, 3/1, 4/1, 3/2, 2/3, 1/4, 1/5, 5/1, 6/1, ...) with equivalent fractions removed. [From Ron King (rrking(AT)alaskalife.net), Mar 07 2009]
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REFERENCES
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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 = 0..100000
Index entries for sequences related to Stern's sequences
Index entries for "core" sequences
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FORMULA
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n occurs phi(n) times (cf. A000010).
a(n) = A020652(n - 1)+A020653(n - 1). n = a(A015614(n)) = a(A002088(n)) - 1 = a(A002088(n - 1)) - Henry Bottomley (se16(AT)btinternet.com), Dec 18 2000
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EXAMPLE
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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).
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MAPLE
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with (numtheory): A038567 := proc (n) local sum, k; sum := 1: k := 2: while (sum < n) do: sum := sum + phi(k): k := k + 1: od: RETURN (k-1): end: # from UlrSchimke(AT)aol.com, Nov 06, 2001
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PROGRAM
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(PARI) a(n)=if(n<0, 0, s=1; while(sum(i=1, s, eulerphi(i))<n, s++); s)
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CROSSREFS
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Cf. A020652, A020653, A038566-A038569.
A054427 gives mapping to Stern-Brocot tree.
Sequence in context: A061716 A126236 A073047 this_sequence A036234 A061091 A086592
Adjacent sequences: A038564 A038565 A038566 this_sequence A038568 A038569 A038570
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KEYWORD
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nonn,frac,core,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
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