A285343 - OEIS

%I #8 Apr 25 2017 17:19:41

%S 1,3,4,5,7,9,10,11,13,14,15,17,18,19,21,23,24,25,27,29,30,31,33,34,35,

%T 37,38,39,41,43,44,45,47,48,49,51,52,53,55,57,58,59,61,62,63,65,66,67,

%U 69,71,72,73,75,77,78,79,81,82,83,85,86,87,89,91,92,93

%N Positions of 1 in A285341; complement of A285342.

%C Conjecture: -1 < n*sqrt(2) - a(n) < 1 for n>=1.

%H Clark Kimberling, <a href="/A285343/b285343.txt">Table of n, a(n) for n = 1..10000</a>

%e As a word, A285341 = 1011101..., in which 1 is in positions 1,3,4,5,7,9,...

%t s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {1, 0, 1, 1}}] &, {0}, 10]; (* A285341 *)

%t u = Flatten[Position[s, 0]];  (* A285342 *)

%t Flatten[Position[s, 1]];  (* A285343 *)

%t u/2 (* A285344)

%Y Cf. A285341, A285342, A285344.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Apr 25 2017