Search: id:A003602
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%I A003602 M0145
%S A003602 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,
%T A003602 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,
%U A003602 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
%N A003602 Kimberling's paraphrases: if n = (2k-1)*2^m then a(n) = k.
%C A003602 Fractal sequence obtained from powers of 2.
%C A003602 k occurs at (2k-1)*A000079(k) - Robert G. Wilson v May 23 2006.
%C A003602 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]
%D A003602 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003602 J.-P. Allouche and J. Shallit, The ring of k-regular sequences, II, Theoret. 
               Computer Sci., 307 (2003), 3-29.
%D A003602 J.-P. Delahaye, L'arithmetique geometrique, Pour la Science, No. 360, 
               October 2007.
%D A003602 C. Kimberling, Numeration systems and fractal sequences, Acta Arithmetica 
               73 (1995) 103-117.
%H A003602 N. J. A. Sloane, <a href="b003602.txt">Table of n, a(n) for n = 1..10000</
               a>
%H A003602 J.-P. Allouche and J. Shallit, <a href="http://www.lri.fr/~allouche/kreg2.ps">
               The Ring of k-regular Sequences, II</a>
%H A003602 C. Kimberling, <a href="http://faculty.evansville.edu/ck6/integer/fractals.html">
               Fractal sequences</a>
%H A003602 R. Stephan, <a href="somedcgf.html">Some divide-and-conquer sequences 
               ...</a>
%H A003602 R. Stephan, <a href="a079944.ps">Table of generating functions</a>
%F A003602 Inverse Weigh transform of A035528 (Christian Bower (bowerc(AT)usa.net)).
%F A003602 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
%F A003602 a(2n-1) = n and a(2n) = a(n) - Pab Ter (pabrlos2(AT)yahoo.com), Oct 25 
               2005
%F A003602 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
%F A003602 Ordinal transform of A001511. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), 
               Aug 28 2006
%p A003602 A003602:=proc(n) options remember: if n mod 2 = 1 then RETURN((n+1)/2) 
               else RETURN(A003602(n/2)) fi: end; (Pab Ter)
%p A003602 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)];
%t A003602 f[n_] := Block[{m = n}, While[ EvenQ@m, m /= 2]; (m + 1)/2]; Array[a, 
               84] (* or *)
%t A003602 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)
%Y A003602 Cf. A003603. Equals (A000265 + 1)/2.
%Y A003602 Cf. A117303, A101279.
%Y A003602 Sequence in context: A124223 A094193 A108712 this_sequence A049773 A123021 
               A028914
%Y A003602 Adjacent sequences: A003599 A003600 A003601 this_sequence A003603 A003604 
               A003605
%K A003602 nonn,easy,nice
%O A003602 1,3
%A A003602 N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein
%E A003602 More terms from Pab Ter (pabrlos2(AT)yahoo.com), Oct 25 2005

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