Search: id:A003603
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%I A003603 M0138
%S A003603 1,1,1,2,1,3,2,1,4,3,2,5,1,6,4,3,7,2,8,5,1,9,6,4,10,3,11,7,2,12,8,5,13,
%T A003603 1,14,9,6,15,4,16,10,3,17,11,7,18,2,19,12,8,20,5,21,13,1,22,14,9,23,6,
%U A003603 24,15,4,25,16,10,26,3,27,17,11,28,7,29,18,2,30,19,12,31,8,32,20,5,33
%N A003603 Fractal sequence obtained from Fibonacci numbers (or Wythoff array).
%D A003603 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003603 C. Kimberling, Numeration systems and fractal sequences, Acta Arithmetica 
               73 (1995) 103-117.
%H A003603 C. Kimberling, <a href="http://faculty.evansville.edu/ck6/integer/fractals.html">
               Fractal sequences</a>
%H A003603 N. J. A. Sloane, <a href="classic.html#WYTH">Classic Sequences</a>
%F A003603 Vertical para-budding sequence: says which row of Wythoff array (starting 
               row count at 1) contains n.
%F A003603 If delete first occurrence of 1, 2, 3, ... the sequence is unchanged.
%F A003603 Contribution from Clark Kimberling (ck6(AT)evansville.edu), Oct 29 2009: 
               (Start)
%F A003603 The fractal sequence of the Wythoff array can be constructed without
%F A003603 reference to the Wythoff array or Fibonacci numbers. Write initial rows:
%F A003603 Row 1: .... 1
%F A003603 Row 2: .... 1
%F A003603 Row 3: .... 1..2
%F A003603 Row 4: .... 1..3..2
%F A003603 For n>4, to form row n+1, let k be the least positive integer not yet
%F A003603 used; write row n, and right after the 1st number that is also in row 
               n-1,
%F A003603 place k; right after the next number that is also in row n-1, place k+1,
%F A003603 and continue. A003603 is the concatentation of the rows. (End)
%e A003603 Contribution from Clark Kimberling (ck6(AT)evansville.edu), Oct 29 2009: 
               (Start)
%e A003603 In the recurrence for making new rows, we get row 5 from row 4 thus:
%e A003603 Write row 4: 1,3,2, and then place 4 right after 1, and place 5 right
%e A003603 after 2, getting 1,4,3,2,5. (End)
%Y A003603 Equals A019586(n) + 1. Cf. A003602.
%Y A003603 Sequence in context: A167287 A007336 A133334 this_sequence A135227 A104325 
               A133084
%Y A003603 Adjacent sequences: A003600 A003601 A003602 this_sequence A003604 A003605 
               A003606
%K A003603 nonn,easy,nice,eigen
%O A003603 1,4
%A A003603 N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein
%E A003603 More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 
               29 2003

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