%I #12 Nov 22 2024 06:18:47

%S 3,9,12,19,25,28,31,37,40,47,53,59,62,69,75,78,81,87,90,97,100,107,

%T 113,116,119,125,128,135,141,147,150,157,163,166,169,175,181,184,187,

%U 193,196,203,209,215,218,225,231,234,237,243,246,253,256,263,269,272

%N Positions of 1 in A286939; complement of A285432.

%C Conjecture: lim_{n->oo} a(n)/n = 4.89..., and if m denotes this number, then -1 < a(n)/n - m < 2 for n >= 1.

%H Clark Kimberling, <a href="/A285564/b285564.txt">Table of n, a(n) for n = 1..10000</a>

%t s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];

%t w[n_] := StringReplace[w[n - 1], {"00" -> "001", "1" -> "000"}]

%t Table[w[n], {n, 0, 8}]

%t st = ToCharacterCode[w[11]] - 48 (* A286939 *)

%t Flatten[Position[st, 0]] (* A285432 *)

%t Flatten[Position[st, 1]] (* A285564 *)

%t Table[StringLength[w[n]], {n, 1, 35}] (* A285665 conjectured *)

%Y Cf. A286939, A285432, A285665.

%K nonn,easy,changed

%O 1,1

%A _Clark Kimberling_, Jun 04 2017

%E Definition corrected by _Georg Fischer_, Jun 05 2020