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 A191428 Dispersion of ([nr+r]), where r=(golden ratio)=(1+sqrt(5))/2 and [ ]=floor, by antidiagonals. 1
 1, 3, 2, 6, 4, 5, 11, 8, 9, 7, 19, 14, 16, 12, 10, 32, 24, 27, 21, 17, 13, 53, 40, 45, 35, 29, 22, 15, 87, 66, 74, 58, 48, 37, 25, 18, 142, 108, 121, 95, 79, 61, 42, 30, 20, 231, 176, 197, 155, 129, 100, 69, 50, 33, 23, 375, 286, 320, 252, 210, 163, 113, 82, 55, 38, 26, 608, 464, 519, 409, 341, 265, 184, 134, 90, 63, 43, 28 (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.  Examples: (1) s=A000040 (the primes), D=A114537, u=A114538. (2) s=A022343 (without initial 0), D=A035513 (Wythoff array), u=A003603. (3) s=A007067, D=A035506 (Stolarsky array), u=A133299. More recent examples of dispersions: A191426-A191455. LINKS EXAMPLE Northwest corner: 1...3...6...11..19 2...4...8...14..24 5...9...16..27..45 7...12..21..35..58 10..17..29..48..79 MATHEMATICA (* Program generates the dispersion array T of increasing sequence f[n] *) r = 40; r1 = 12;  (* r=# rows of T, r1=# rows to show *) c = 40; c1 = 12;  (* c=# cols of T, c1=# cols to show *) x = GoldenRatio; f[n_] := Floor[n*x + x] (* f(n) is complement of column 1 *) mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1,   Length[Union[list]]] rows = {NestList[f, 1, c]}; Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}]; t[i_, j_] := rows[[i, j]]; TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]] (* A191428 array *) Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191428 sequence *) (* Program by Peter J. C. Moses, Jun 01 2011 *) CROSSREFS Cf. A114537, A035513, A035506. Sequence in context: A274315 A194059 A191427 * A191733 A191444 A258241 Adjacent sequences:  A191425 A191426 A191427 * A191429 A191430 A191431 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Jun 03 2011 STATUS approved

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Last modified January 20 21:46 EST 2022. Contains 350472 sequences. (Running on oeis4.)