%I A019586
%S A019586 0,0,0,1,0,2,1,0,3,2,1,4,0,5,3,2,6,1,7,4,0,8,5,3,9,2,10,6,1,11,7,4,12,
               0,
%T A019586 13,8,5,14,3,15,9,2,16,10,6,17,1,18,11,7,19,4,20,12,0,21,13,8,22,5,23,
%U A019586 14,3,24,15,9,25,2,26,16,10,27,6,28,17,1,29,18,11,30,7,31,19,4,32,20,12
%N A019586 Vertical para-Fibonacci sequence: takes value i on later (i.e. b_j, j 
               >= 2) terms of i-th Fibonacci sequence defined by b_0 = i, b_1 = 
               [ tau(i+1) ].
%C A019586 Gives number of row in Wythoff array that contains n. - Casey Mongoven 
               (cm(AT)caseymongoven.com), Sep 10 2005
%C A019586 Contribution from Clark Kimberling (ck6(AT)evansville.edu), Oct 29 2009: 
               (Start)
%C A019586 For a method of generating this sequence that does not refer to the
%C A019586 Wythoff array or Fibonacci numbers, see A003603. (End)
%D A019586 J. H. Conway, personal communication.
%H A019586 N. J. A. Sloane, <a href="http://www.research.att.com/~njas/doc/sg.txt">
               My favorite integer sequences</a>, in Sequences and their Applications 
               (Proceedings of SETA '98).
%H A019586 N. J. A. Sloane, <a href="classic.html#WYTH">Classic Sequences</a>
%F A019586 Says which row of Wythoff array (starting row count at 0) contains n.
%F A019586 If delete first occurrence of 0, 1, 2, 3, ... the sequence is unchanged.
%Y A019586 Equals A003603(n) - 1.
%Y A019586 Cf. Wythoff array: A035513.
%Y A019586 Sequence in context: A025648 A025655 A022336 this_sequence A063942 A106384 
               A094314
%Y A019586 Adjacent sequences: A019583 A019584 A019585 this_sequence A019587 A019588 
               A019589
%K A019586 nonn,nice,easy,eigen,new
%O A019586 1,6
%A A019586 N. J. A. Sloane (njas(AT)research.att.com) and J. H. Conway (conway(AT)math.princeton.edu)
%E A019586 Casey Mongoven (CaseyBach(AT)aol.com) reports that where the sequence 
               reads 15,9,2,16,10,6,29,1,30,11,7,19..., the 29 and 30 should be 
               17 and 18.
%E A019586 More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 
               29 2003