A285085 - OEIS

%I #4 Apr 20 2017 09:23:48

%S 1,4,5,7,8,10,11,12,15,16,17,19,22,23,25,26,27,30,31,33,34,36,37,38,

%T 40,43,44,46,47,48,51,52,54,55,57,58,59,61,64,65,67,68,69,72,73,75,76,

%U 77,80,81,83,84,86,87,88,91,92,93,95,98,99,101,102,103,106

%N Positions of 1 in A285083; complement of A285084.

%C Conjecture: -1 < n*r - a(n) < 1 for n>=1, where r = (1+sqrt(5))/2, the golden ratio (A001622).

%H Clark Kimberling, <a href="/A285085/b285085.txt">Table of n, a(n) for n = 1..10000</a>

%e As a word, A285083 = 1001101101110..., in which 0 is in positions 2,3,6,9,13,...

%t s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {0, 1, 1}}] &, {0}, 13]; (* A285083 *)

%t Flatten[Position[s, 0]];  (* A285084 *)

%t Flatten[Position[s, 1]];  (* A285085 *)

%Y Cf. A001622, A285080, A285083, A285084.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Apr 19 2017