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A191443
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Dispersion of ([n*sqrt(3)+1]), where [ ]=floor, by antidiagonals.
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1
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=1..62.
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EXAMPLE
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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
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MATHEMATICA
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(* 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 *)
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CROSSREFS
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Cf. A114537, A035513, A035506, A191442.
Sequence in context: A090894 A175004 A191734 * A136175 A129258 A104650
Adjacent sequences: A191440 A191441 A191442 * A191444 A191445 A191446
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling, Jun 04 2011
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STATUS
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approved
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