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%I #54 Aug 22 2021 13:27:42
%S 0,1,0,1,1,0,1,0,1,1,0,1,1,1,0,1,0,1,1,0,1,1,0,1,0,1,1,0,1,1,1,0,1,0,
%T 1,1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,1,1,0,1,1,0,1,0,1,1,0,1,1,1,0,1,0,1,
%U 1,0,1,1,0,1,1,0,1,1,1,0,1,0,1,1,0,1,1,0,1,0,1,1,0,1,1,1,0,1,0,1,1,0,1,0,1
%N Sequence is limit_{t->oo} s_t, where s_k = s_{k-1},s_{k-1}[k-1..end] starting with s_0 = s_0[0..1] = 0,1.
%C A nonperiodic sequence of 0 and 1.
%H Kevin Ryde, <a href="http://user42.tuxfamily.org/seq-A334820/index.html">PARI/GP code and explanation</a>.
%p s:= proc(n) option remember; `if`(n=0, [0, 1][],
%p (l-> [l[], l[n..-1][]][])([s(n-1)]))
%p end:
%p s(10); # gives 1035 = A005126(10) terms; # _Alois P. Heinz_, May 12 2020
%t a[n_] := If[n<2, n, Module[{k = Floor@Log[2, n], m = n}, m-=k+1; While[k >= 0, If[BitGet[m, k]==0, m++; If[BitGet[m, k]==1, Return[1]]]; k--]]; 0];
%t a /@ Range[0, 104] (* _Jean-François Alcover_, Nov 16 2020, after _Kevin Ryde_ *)
%o (PARI) a(n) = { if(n, my(k=logint(n,2)); n-=k+1; while(k>=0, if(!bittest(n,k), n++; if(bittest(n,k), return(1))); k--)); 0; } \\ _Kevin Ryde_, Jun 26 2020
%Y Cf. A005126 (s lengths), A057215.
%K nonn
%O 0,1
%A _Richard Aime Blavy_, May 12 2020
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