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 A248514 Fractal sequence of the dispersion of the "odious numbers". 2
 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, 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, 29, 30, 15, 31, 16, 8, 32, 1, 33, 34, 17, 35, 18, 9, 36, 37, 19 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS As a fractal sequence, it contains infinitely many copies of itself: removing the first occurence of each number leaves the original sequence. REFERENCES Clark Kimberling, "Fractal sequences and interspersions," Ars Combinatoria 45 (1997) 157-168. LINKS Clark Kimberling, Table of n, a(n) for n = 1..200 EXAMPLE A northwest corner of the dispersion (A248513) of the "odious numbers" (A181155) follows: 1 ... 2 ... 3 ... 5 ... 9 ... 17 .... 33 4 ... 8 ... 15 .. 29 .. 57 .. 113 ... 225 6 ... 12 .. 23 .. 45 .. 89 .. 177 ... 353 7 ... 14 .. 27 .. 53 .. 105 .. 209 .. 417 10 .. 20 .. 39 .. 77 .. 153 .. 305 .. 609 The numbers 1, 2, 3, 4, 5 appear in rows 1, 1, 1, 2, 1, respectively, so that A248514 = (1, 1, 1, 2, 1, ...). MATHEMATICA r = 40; r1 = 10; (* r = # rows of T, r1 = # rows to show*); c = 40; c1 = 12; (* c = # cols of T, c1 = # cols to show*); x = GoldenRatio; s[n_] := s[n] = If[n < 1, 0, 2 n - Mod[Total[IntegerDigits[n - 1, 2]], 2]]; mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1,   Length[Union[list]]]; rows = {NestList[s, 1, c]}; Do[rows = Append[rows, NestList[s, mex[Flatten[rows]], r]], {r}]; t[i_, j_] := rows[[i, j]]; TableForm[Table[t[i, j], {i, 1, r1}, {j, 1, c1}]] (* A248513 array*) u = Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]]  (* A248013 sequence*) row[i_] := row[i] = Table[t[i, j], {j, 1, c}] f[n_] := Select[Range[r], MemberQ[row[#], n] &] v = Flatten[Table[f[n], {n, 1, 200}]]  (* A248514 *) CROSSREFS Cf. A248513. Sequence in context: A125158 A273823 A112384 * A123390 A162598 A088208 Adjacent sequences:  A248511 A248512 A248513 * A248515 A248516 A248517 KEYWORD nonn,easy AUTHOR Clark Kimberling, Oct 08 2014 STATUS approved

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