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A248514 Fractal sequence of the dispersion of the "odious numbers".

%I A248514 #8 Feb 22 2020 20:54:24
%S A248514 1,1,1,2,1,3,4,2,1,5,6,3,7,4,2,8,1,9,10,5,11,6,3,12,13,7,4,14,2,15,16,
%T A248514 8,1,17,18,9,19,10,5,20,21,11,6,22,3,23,24,12,25,13,7,26,4,27,28,14,2,
%U A248514 29,30,15,31,16,8,32,1,33,34,17,35,18,9,36,37,19
%N A248514 Fractal sequence of the dispersion of the "odious numbers".
%C A248514 As a fractal sequence, it contains infinitely many copies of itself: removing the first occurrence of each number leaves the original sequence.
%D A248514 Clark Kimberling, "Fractal sequences and interspersions," Ars Combinatoria 45 (1997) 157-168.
%H A248514 Clark Kimberling, <a href="/A248514/b248514.txt">Table of n, a(n) for n = 1..200</a>
%e A248514 A northwest corner of the dispersion (A248513) of the "odious numbers" (A181155) follows:
%e A248514 1 ... 2 ... 3 ... 5 ... 9 ... 17 .... 33
%e A248514 4 ... 8 ... 15 .. 29 .. 57 .. 113 ... 225
%e A248514 6 ... 12 .. 23 .. 45 .. 89 .. 177 ... 353
%e A248514 7 ... 14 .. 27 .. 53 .. 105 .. 209 .. 417
%e A248514 10 .. 20 .. 39 .. 77 .. 153 .. 305 .. 609
%e A248514 The numbers 1, 2, 3, 4, 5 appear in rows 1, 1, 1, 2, 1, respectively, so that A248514 = (1, 1, 1, 2, 1, ...).
%t A248514 r = 40; r1 = 10; (* r = # rows of T, r1 = # rows to show*);
%t A248514 c = 40; c1 = 12; (* c = # cols of T, c1 = # cols to show*);
%t A248514 x = GoldenRatio; s[n_] := s[n] = If[n < 1, 0, 2 n - Mod[Total[IntegerDigits[n - 1, 2]], 2]];
%t A248514 mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1,   Length[Union[list]]]; rows = {NestList[s, 1, c]};
%t A248514 Do[rows = Append[rows, NestList[s, mex[Flatten[rows]], r]], {r}];
%t A248514 t[i_, j_] := rows[[i, j]]; TableForm[Table[t[i, j], {i, 1, r1}, {j, 1, c1}]] (* A248513 array*)
%t A248514 u = Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]]  (* A248013 sequence*)
%t A248514 row[i_] := row[i] = Table[t[i, j], {j, 1, c}]
%t A248514 f[n_] := Select[Range[r], MemberQ[row[#], n] &]
%t A248514 v = Flatten[Table[f[n], {n, 1, 200}]]  (* A248514 *)
%Y A248514 Cf. A248513.
%K A248514 nonn,easy
%O A248514 1,4
%A A248514 _Clark Kimberling_, Oct 08 2014