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A247636 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.

%I A247636 #10 Sep 26 2014 21:14:03
%S A247636 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 A247636 56,60,61,64,65,66,68,70,71,72,77,78,80,83,84,86,88,89,91,93,95,96,99,
%U A247636 100,101,102,103,104,105,107,108,109,110,111,112,113,118
%N A247636 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 A247636 Every positive integer lies in exactly one of the sequences A247635 and A247636.
%H A247636 Clark Kimberling, <a href="/A247636/b247636.txt">Table of n, a(n) for n = 1..1000</a>
%e A247636 r has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, ...
%e A247636 s has binary digits 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, ...
%e A247636 so that a(1) = 1 and a(2) = 3.
%t A247636 z = 200; r = FractionalPart[Sqrt[2]]; s = FractionalPart[Sqrt[8]];
%t A247636 u = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[r, 2, z]];
%t A247636 v = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[s, 2, z]];
%t A247636 t = Table[If[u[[n]] == v[[n]], 1, 0], {n, 1, z}];
%t A247636 Flatten[Position[t, 1]]  (* A247635 *)
%t A247636 Flatten[Position[t, 0]]  (* A247636 *)
%Y A247636 Cf. A247635, A247632, A247524.
%K A247636 nonn,easy,base
%O A247636 1,2
%A A247636 _Clark Kimberling_, Sep 23 2014