%I #10 Sep 26 2014 21:14:03

%S 1,3,4,5,6,7,12,13,15,19,21,23,25,27,29,36,38,41,42,46,48,50,52,53,55,

%T 56,60,61,64,65,66,68,70,71,72,77,78,80,83,84,86,88,89,91,93,95,96,99,

%U 100,101,102,103,104,105,107,108,109,110,111,112,113,118

%N Numbers k such that d(r,k) != d(s,k), where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(8)}, and { } = fractional part.

%C Every positive integer lies in exactly one of the sequences A247635 and A247636.

%H Clark Kimberling, <a href="/A247636/b247636.txt">Table of n, a(n) for n = 1..1000</a>

%e r has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, ...

%e s has binary digits 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, ...

%e so that a(1) = 1 and a(2) = 3.

%t z = 200; r = FractionalPart[Sqrt[2]]; s = FractionalPart[Sqrt[8]];

%t u = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[r, 2, z]];

%t v = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[s, 2, z]];

%t t = Table[If[u[[n]] == v[[n]], 1, 0], {n, 1, z}];

%t Flatten[Position[t, 1]] (* A247635 *)

%t Flatten[Position[t, 0]] (* A247636 *)

%Y Cf. A247635, A247632, A247524.

%K nonn,easy,base

%O 1,2

%A _Clark Kimberling_, Sep 23 2014