A167198 - OEIS

%I #14 May 04 2016 19:03:48

%S 1,1,2,1,2,3,1,4,2,3,5,1,4,6,2,7,3,5,8,1,9,4,6,10,2,7,11,3,12,5,8,13,

%T 1,9,14,4,15,6,10,16,2,17,7,11,18,3,12,19,5,20,8,13,21,1,22,9,14,23,4,

%U 15,24,6,25,10,16,26,2,17,27,7,28,11,18,29,3,30,12,19,31,5,20,32,8,33,13

%N Fractal sequence of the interspersion A083047.

%C As a fractal sequence, if the first occurrence of each term is deleted, the remaining sequence is the original. In general, the interspersion of a fractal sequence is constructed by rows: row r consists of all n, such that a(n)=r; in particular, A083047 is constructed in this way from A167198.

%C a(n-1) gives the row number which contains n in the dual Wythoff array A126714 (beginning the row count at 1), see also A223025 and A019586. - _Casey Mongoven_, Mar 11 2013

%D Clark Kimberling, Stolarsky interspersions, Ars Combinatoria 39 (1995), 129-138.

%H Clark Kimberling, <a href="http://www.fq.math.ca/Scanned/32-4/kimberling.pdf">The first column of an interspersion</a>, The Fibonacci Quarterly 32 (1994), 301-315.

%F Following is a construction that avoids reference to A083047.

%F Write initial rows:

%F Row 1: .... 1

%F Row 2: .... 1

%F Row 3: .... 2..1

%F Row 4: .... 2..3..1

%F For n>=4, to form row n+1, let k be the least positive integer not yet used; write row n, and right before the first number that is also in row n-1, place k; right before the next number that is also in row n-1, place k+1, and continue. A167198 is the concatenation of the rows. (If "before" is replaced by "after", the resulting fractal sequence is A003603, and the associated interspersion is the Wythoff array, A035513.)

%e To produce row 5, first write row 4: 2,3,1, then place 4 right before 2, and then place 5 right before 1, getting 4,2,3,5,1.

%Y Cf. A003603, A083047, A035513, A000045.

%K nonn

%O 1,3

%A _Clark Kimberling_, Oct 30 2009