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A288998 Positions of 0 in A288997; complement of A288999.

%I A288998 #7 Feb 06 2025 12:23:05
%S A288998 1,2,4,5,6,8,9,11,12,13,15,16,18,19,21,22,23,25,26,28,29,30,32,33,35,
%T A288998 36,38,39,40,42,43,45,46,47,49,50,52,53,54,56,57,59,60,62,63,64,66,67,
%U A288998 69,70,71,73,74,76,77,79,80,81,83,84,86,87,88,90,91,93
%N A288998 Positions of 0 in A288997; complement of A288999.
%C A288998 Conjecture:  a(n)/n -> sqrt(2), and 0 < sqrt(2) - a(n)/n < -1 + sqrt(2) for n >= 1.
%H A288998 Clark Kimberling, <a href="/A288998/b288998.txt">Table of n, a(n) for n = 1..10000</a>
%F A288998 a(n) = round((n-1/2)*sqrt(2)) (conjectured). - _Chai Wah Wu_, Feb 06 2025
%t A288998 z = 10; (* number of iterates *)
%t A288998 s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
%t A288998 w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "001", "10" -> "001"}]
%t A288998 TableForm[Table[w[n], {n, 0, 10}]]
%t A288998 st = ToCharacterCode[w[z]] - 48   (* A288997 *)
%t A288998 Flatten[Position[st, 0]]  (* A288998 *)
%t A288998 Flatten[Position[st, 1]]  (* A288999 *)
%Y A288998 Cf. A288997, A288999.
%K A288998 nonn,easy
%O A288998 1,2
%A A288998 _Clark Kimberling_, Jun 25 2017