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%I #14 Oct 27 2023 13:10:12
%S 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,
%T 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,
%U 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
%N 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.
%H Michael S. Branicky, <a href="/A108736/b108736.txt">Table of n, a(n) for n = 1..10001</a>
%e We construct S as follows, starting with S = {}.
%e 0 is missing, so S = {0};
%e 1 is missing, so S = {0,1};
%e 00 is missing, so S = {0,1,0,0};
%e 01 and 10 are now visible, but 11 is missing, so S = {0,1,0,0,1,1};
%e 000 is missing, so S = {0,1,0,0,1,1,0,0,0}; etc.
%p 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
%o (Python)
%o from itertools import count, islice, product
%o def a(): # generator of terms
%o S = ""
%o for Sm in ("".join(w) for i in count(1) for w in product("01", repeat=i)):
%o if Sm in S: continue
%o for i in range(1, len(Sm)+1):
%o v = Sm[-i:]
%o t = "" if len(v) == len(Sm) else S[-len(Sm)+i:]
%o if t+v == Sm: break
%o S += v
%o yield from list(map(int, v))
%o print(list(islice(a(), 105))) # _Michael S. Branicky_, Oct 27 2023
%Y Cf. A108737.
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_, Jun 23 2005
%E More terms from _R. J. Mathar_, Aug 15 2007
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