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 A120873 #25 Sep 17 2022 06:46:17
%S A120873 1,1,2,3,1,4,2,5,6,3,7,8,1,9,4,10,11,2,12,5,13,14,6,15,16,3,17,7,18,
%T A120873 19,8,20,21,1,22,9,23,24,4,25,10,26,27,11,28,29,2,30,12,31,32,5,33,13,
%U A120873 34,35,14,36,37,6,38,15,39,40,16,41,42,3,43,17,44,45,7,46,18,47,48,19,49
%N A120873 Fractal sequence of the Wythoff difference array (A080164).
%C A120873 A fractal sequence f contains itself as a proper subsequence; e.g., if you delete the first occurrence of each positive integer, the remaining sequence is f; thus f properly contains itself infinitely many times.
%C A120873 This is subsequence of A003603. - _Clark Kimberling_, Oct 26 2021
%C A120873 a(n) is the number of the row of the Wythoff array (A035513) that contains the n-th Wythoff pair; e.g., the 6th Wythoff pair is (floor(6*r), floor(6*r^2)), where r = golden ratio = A001622, which is in row 4 of the Wythoff array. - _Clark Kimberling_, Oct 26 2021
%D A120873 Clark Kimberling, The Wythoff difference array, in Applications of Fibonacci Numbers, vol.10, Proceedings of the Eleventh International Conference on Fibonacci Numbers and Their Applications, William Webb, editor, Congressus Numerantium, Winnipeg, Manitoba 194 (2009) 153-158.
%H A120873 Michel Marcus, <a href="/A120873/b120873.txt">Table of n, a(n) for n = 1..10000</a>
%H A120873 N. J. A. Sloane, <a href="/classic.html#WYTH">Classic Sequences</a>.
%e A120873 The fractal sequence f(n) of a dispersion D={d(g,h,)} is defined as follows.
%e A120873 For each positive integer n there is a unique (g,h) such that n=d(g,h) and f(n)=g. So f(7)=2 because the row of the WDA in which 7 occurs is row 2.
%o A120873 (PARI) lowerw(n) = (n+sqrtint(5*n^2))\2 ; \\ A000201
%o A120873 upperw(n) = (sqrtint(n^2*5)+n*3)\2; \\ A001950
%o A120873 compoundw(n) = (sqrtint(n^2*5)+n*3)\2 - 1; \\ A003622
%o A120873 a(n) = my(x=lowerw(n), y=upperw(n), u); while (1, my(k=1, ok=1); while(ok, my(xx = lowerw(k), yy = compoundw(k)); if ((x == xx) && (y == yy), return(k)); if (xx > x, ok = 0); k++;); u = x; x = y - u; y = u;); \\ _Michel Marcus_, Sep 17 2022
%Y A120873 Cf. A001622, A003603, A035513, A080164.
%K A120873 nonn
%O A120873 1,3
%A A120873 _Clark Kimberling_, Jul 10 2006