This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A167198 #16 Jan 05 2025 19:51:39 %S A167198 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 A167198 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 A167198 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 A167198 Fractal sequence of the interspersion A083047. %C A167198 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 A167198 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 A167198 Clark Kimberling, Stolarsky interspersions, Ars Combinatoria 39 (1995), 129-138. %H A167198 Clark Kimberling, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/32-4/kimberling.pdf">The first column of an interspersion</a>, The Fibonacci Quarterly 32 (1994), 301-315. %F A167198 Following is a construction that avoids reference to A083047. %F A167198 Write initial rows: %F A167198 Row 1: .... 1 %F A167198 Row 2: .... 1 %F A167198 Row 3: .... 2..1 %F A167198 Row 4: .... 2..3..1 %F A167198 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 A167198 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 A167198 Cf. A003603, A083047, A035513, A000045. %K A167198 nonn %O A167198 1,3 %A A167198 _Clark Kimberling_, Oct 30 2009