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 A191443 Dispersion of ([n*sqrt(3)+1]), where [ ]=floor, by antidiagonals. 1
 1, 2, 3, 4, 6, 5, 7, 11, 9, 8, 13, 20, 16, 14, 10, 23, 35, 28, 25, 18, 12, 40, 61, 49, 44, 32, 21, 15, 70, 106, 85, 77, 56, 37, 26, 17, 122, 184, 148, 134, 97, 65, 46, 30, 19, 212, 319, 257, 233, 169, 113, 80, 52, 33, 22, 368, 553, 446, 404, 293, 196, 139 (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....2....4....7....13 3....6....11...20...35 5....9....16...28...49 8....14...25...44...77 10...18...32...56...97 MATHEMATICA (* Program generates the dispersion array T of increasing sequence f[n] *) r=40; r1=12; c=40; c1=12;  x = Sqr[3]; f[n_] := Floor[n*x+1] (* 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}]] (* A191443 array *) Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191443 sequence *) (* Program by Peter Moses, June 1, 2011 *) CROSSREFS Cf. A114537, A035513, A035506, A191442. Sequence in context: A090894 A175004 A191734 * A136175 A129258 A104650 Adjacent sequences:  A191440 A191441 A191442 * A191444 A191445 A191446 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Jun 04 2011 STATUS approved

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Last modified May 23 13:42 EDT 2013. Contains 225590 sequences.