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A247460 Numbers k such that d(r,k) != d(s,k), where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {3*sqrt(2)}, and { } = fractional part.

%I A247460 #12 Sep 28 2014 09:11:28
%S A247460 2,4,6,12,14,18,20,22,24,26,28,35,37,41,45,47,49,52,55,60,63,65,67,69,
%T A247460 71,77,79,83,85,88,90,92,95,98,100,102,104,106,108,110,112,117,119,
%U A247460 121,126,129,133,135,138,143,145,150,152,155,157,159,163,166,168
%N A247460 Numbers k such that d(r,k) != d(s,k), where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {3*sqrt(2)}, and { } = fractional part.
%C A247460 Every positive integer lies in exactly one of the sequences A247459 and A247460.
%H A247460 Clark Kimberling, <a href="/A247460/b247460.txt">Table of n, a(n) for n = 1..500</a>
%e A247460 {1*sqrt(2)} has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1,...
%e A247460 {3*sqrt(2)} has binary digits 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1,...
%e A247460 so that a(1) = 2 and a(2) = 4.
%t A247460 z = 200; r = FractionalPart[Sqrt[2]]; s = FractionalPart[3*Sqrt[2]];
%t A247460 u = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[r, 2, z]];
%t A247460 v = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[s, 2, z]];
%t A247460 t = Table[If[u[[n]] == v[[n]], 1, 0], {n, 1, z}];
%t A247460 Flatten[Position[t, 1]]  (* A247459 *)
%t A247460 Flatten[Position[t, 0]]  (* A247460 *)
%Y A247460 Cf. A247459, A247455, A247454.
%K A247460 nonn,easy,base
%O A247460 1,1
%A A247460 _Clark Kimberling_, Sep 18 2014