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A247459 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 A247459 #12 Sep 28 2014 08:41:46
%S A247459 1,3,5,7,8,9,10,11,13,15,16,17,19,21,23,25,27,29,30,31,32,33,34,36,38,
%T A247459 39,40,42,43,44,46,48,50,51,53,54,56,57,58,59,61,62,64,66,68,70,72,73,
%U A247459 74,75,76,78,80,81,82,84,86,87,89,91,93,94,96,97,99,101
%N A247459 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 A247459 Every positive integer lies in exactly one of the sequences A247459 and A247460.
%H A247459 Clark Kimberling, <a href="/A247459/b247459.txt">Table of n, a(n) for n = 1..1000</a>
%e A247459 {1*sqrt(2)} has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1,...
%e A247459 {3*sqrt(2)} has binary digits 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1,...
%e A247459 so that a(1) = 1 and a(2) = 3.
%t A247459 z = 200; r = FractionalPart[Sqrt[2]]; s = FractionalPart[3*Sqrt[2]];
%t A247459 u = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[r, 2, z]];
%t A247459 v = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[s, 2, z]];
%t A247459 t = Table[If[u[[n]] == v[[n]], 1, 0], {n, 1, z}];
%t A247459 Flatten[Position[t, 1]]  (* A247459 *)
%t A247459 Flatten[Position[t, 0]]  (* A247460 *)
%Y A247459 Cf. A247460, A247455, A247454.
%K A247459 nonn,easy,base
%O A247459 1,2
%A A247459 _Clark Kimberling_, Sep 18 2014