A285303 - OEIS

%I #7 Nov 22 2024 06:19:59

%S 3,4,6,9,13,14,18,20,22,26,28,31,34,38,40,43,47,48,52,53,57,59,62,66,

%T 67,71,73,75,79,81,83,87,89,92,96,97,101,103,105,109,111,114,117,121,

%U 123,126,129,133,135,138,142,143,147,149,151,155,157,160,163,167

%N Positions of 1 in A284932; complement of A285303.

%C Conjecture: lim_{n->oo} a(n)/n = 0.78..., and if m denotes this number, then -1 < a(n)/n - m < 1 for n >= 1.

%H Clark Kimberling, <a href="/A285303/b285303.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" -> "10"}]

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

%t st = ToCharacterCode[w[11]] - 48   (* A284932 *)

%t Flatten[Position[st, 0]]  (* A285352 *)

%t Flatten[Position[st, 1]]  (* A285303 *)

%t Table[StringLength[w[n]], {n, 1, 35}] (* A286938 *)

%Y Cf. A284932, A285352, A286938.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Jun 03 2017