cp's OEIS Frontend

A288999 Positions of 1 in A288997; complement of A288998.

%I A288999 #7 Feb 06 2025 12:23:12
%S A288999 3,7,10,14,17,20,24,27,31,34,37,41,44,48,51,55,58,61,65,68,72,75,78,
%T A288999 82,85,89,92,96,99,102,106,109,113,116,119,123,126,130,133,136,140,
%U A288999 143,147,150,154,157,160,164,167,171,174,177,181,184,188,191,195,198
%N A288999 Positions of 1 in A288997; complement of A288998.
%C A288999 Conjecture:  a(n)/n -> 2 + sqrt(2), and -1 < 2 + sqrt(2) - a(n)/n < -1 + sqrt(2) for n >= 1.
%H A288999 Clark Kimberling, <a href="/A288999/b288999.txt">Table of n, a(n) for n = 1..10000</a>
%F A288999 a(n) = 2n+round(n*sqrt(2)) (conjectured). - _Chai Wah Wu_, Feb 06 2025
%t A288999 z = 10; (* number of iterates *)
%t A288999 s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
%t A288999 w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "001", "10" -> "001"}]
%t A288999 TableForm[Table[w[n], {n, 0, 10}]]
%t A288999 st = ToCharacterCode[w[z]] - 48   (* A288997 *)
%t A288999 Flatten[Position[st, 0]]  (* A288998 *)
%t A288999 Flatten[Position[st, 1]]  (* A288999 *)
%Y A288999 Cf. A288997, A288998.
%K A288999 nonn,easy
%O A288999 1,1
%A A288999 _Clark Kimberling_, Jun 25 2017