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A108736
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Start with S = {}. For m = 1, 2, 3, ... in turn, examine all 2^m m-bit strings u in arithmetic order. If u is not a substring of S, append the minimal number of 0's and 1's to S to remedy this. Sequence gives S.
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2
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0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..105.
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EXAMPLE
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We construct S as follows, starting with S = {}.
0 is missing, so S = {0};
1 is missing, so S = {0,1};
00 is missing, so S = {0,1,0,0};
01 and 10 are now visible, but 11 is missing, so S = {0,1,0,0,1,1};
000 is missing, so S = {0,1,0,0,1,1,0,0,0}; etc.
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MAPLE
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bString := proc(n, m) local a, i; a := [] ; for i from m-1 to 0 by -1 do a := [op(a), floor(n/2^i) mod 2] ; od: RETURN(a) ; end: A108736 := proc(nmax) local S, m, b, partoverl, overl, mbstr; S := [] ; m := 1: while nops(S) < nmax do for b from 0 to 2^m-1 do mbstr := bString(b, m) ; if verify(mbstr, S, 'sublist') = false then partoverl := false ; for overl from m-1 to 1 by -1 do if verify(mbstr[1..overl], S[ -overl..-1], 'sublist') = true then S := [op(S), op(mbstr[overl+1..nops(mbstr)])] ; partoverl := true ; break ; fi ; od; if partoverl = false then S := [op(S), op(mbstr)] ; fi ; fi ; od: m := m+1: od: RETURN(S) ; end: op(A108736(80)) ; - R. J. Mathar, Aug 15 2007
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CROSSREFS
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Cf. A108737.
Sequence in context: A071986 A079944 A059652 * A079813 A078580 A059651
Adjacent sequences: A108733 A108734 A108735 * A108737 A108738 A108739
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Jun 23 2005
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EXTENSIONS
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More terms from R. J. Mathar, Aug 15 2007
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STATUS
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approved
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