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 A248513 Rectangular array by antidiagonals: the dispersion of A181155 ("odious numbers"). 4
 1, 2, 4, 3, 8, 6, 5, 15, 12, 7, 9, 29, 23, 14, 10, 17, 57, 45, 27, 20, 11, 33, 113, 89, 53, 39, 22, 13, 65, 225, 177, 105, 77, 43, 26, 16, 129, 449, 353, 209, 153, 85, 51, 32, 18, 257, 897, 705, 417, 305, 169, 101, 63, 36, 19, 513, 1793, 1409, 833, 609, 337 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Background discussion: Suppose that s is an increasing sequence of positive integers, that the complement t of s is infinite, and that t(1) = 1. The dispersion of s is the array D whose n-th row is (t(n), s(t(n)), s(s(t(n)), s(s(s(t(n)))), ...).  Every positive integer occurs exactly once in D, so that, as a sequence, D is a permutation of the positive integers. The sequence u given by u(n) = (number of the row of D that contains n) is a fractal sequence, as in A248514. The n-th term of column 1 is A001969(n) + 1, where A001969 are the "evil numbers". REFERENCES Clark Kimberling, Fractal sequences and interspersions, Ars Combinatoria 45 (1997) 157-168. LINKS Clark Kimberling, Antidiagonals n = 1..60, flattened Clark Kimberling, Interspersions and dispersions, Proceedings of the American Mathematical Society, 117 (1993) 313-321. EXAMPLE Northwest corner: 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 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}]] u = Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A248513 *) 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. A248514. Sequence in context: A232563 A048672 A277517 * A266414 A245613 A260431 Adjacent sequences:  A248510 A248511 A248512 * A248514 A248515 A248516 KEYWORD nonn,tabl,easy AUTHOR Clark Kimberling, Oct 08 2014 STATUS approved

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Last modified December 12 05:15 EST 2018. Contains 318052 sequences. (Running on oeis4.)