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Search: id:A003602
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| A003602 |
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Kimberling's paraphrases: if n = (2k-1)*2^m then a(n) = k.
(Formerly M0145)
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+0
26
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| 1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 7, 4, 8, 1, 9, 5, 10, 3, 11, 6, 12, 2, 13, 7, 14, 4, 15, 8, 16, 1, 17, 9, 18, 5, 19, 10, 20, 3, 21, 11, 22, 6, 23, 12, 24, 2, 25, 13, 26, 7, 27, 14, 28, 4, 29, 15, 30, 8, 31, 16, 32, 1, 33, 17, 34, 9, 35, 18, 36, 5, 37, 19, 38, 10, 39, 20, 40, 3, 41, 21, 42
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Fractal sequence obtained from powers of 2.
k occurs at (2k-1)*A000079(k) - Robert G. Wilson v May 23 2006.
Sequence is T^(infty)(1) where T is acting on a word w=w(1)w(2)..w(m) as follows : T(w)="1"w(1)"2"w(2)"3"(...)"m"w(m)"m+1". For instance T(ab)=1a2b3. Thus T(1)=112, T(T(1))=1121324, T(T(T(1)))=112132415362748. [From Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 02 2009]
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J.-P. Allouche and J. Shallit, The ring of k-regular sequences, II, Theoret. Computer Sci., 307 (2003), 3-29.
J.-P. Delahaye, L'arithmetique geometrique, Pour la Science, No. 360, October 2007.
C. Kimberling, Numeration systems and fractal sequences, Acta Arithmetica 73 (1995) 103-117.
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 1..10000
J.-P. Allouche and J. Shallit, The Ring of k-regular Sequences, II
C. Kimberling, Fractal sequences
R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
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FORMULA
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Inverse Weigh transform of A035528 (Christian Bower (bowerc(AT)usa.net)).
G.f.: 1/x * sum(k>=0, x^2^k/(1-2x^2^(k+1)+x^2^(k+2))). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jul 24 2003
a(2n-1) = n and a(2n) = a(n) - Pab Ter (pabrlos2(AT)yahoo.com), Oct 25 2005
a(A118413(n,k))=A002024(n,k); = a(A118416(n,k))=A002260(n,k); a(A014480(n))=A001511(A014480(n)). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 27 2006
Ordinal transform of A001511. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Aug 28 2006
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MAPLE
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A003602:=proc(n) options remember: if n mod 2 = 1 then RETURN((n+1)/2) else RETURN(A003602(n/2)) fi: end; (Pab Ter)
a:=array(0..10000); a[1]:=1; M:=200; for n from 2 to M do if n mod 2 = 1 then a[n]:=(n+1)/2; else a[n]:=a[n/2]; fi; od: [seq(a[n], n=1..M)];
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MATHEMATICA
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f[n_] := Block[{m = n}, While[ EvenQ@m, m /= 2]; (m + 1)/2]; Array[a, 84] (* or *)
a[1] = 1; a[n_] := a[n] = If[OddQ@n, (n + 1)/2, a[n/2]]; Array[a, 84] (from Robert G. Wilson v (rgwv(at)rgwv.com), May 23 2006)
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CROSSREFS
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Cf. A003603. Equals (A000265 + 1)/2.
Cf. A117303, A101279.
Adjacent sequences: A003599 A003600 A003601 this_sequence A003603 A003604 A003605
Sequence in context: A124223 A094193 A108712 this_sequence A049773 A123021 A028914
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein
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EXTENSIONS
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More terms from Pab Ter (pabrlos2(AT)yahoo.com), Oct 25 2005
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