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A247635 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 A247635 #12 Jan 03 2024 07:42:56
%S A247635 2,8,9,10,11,14,16,17,18,20,22,24,26,28,30,31,32,33,34,35,37,39,40,43,
%T A247635 44,45,47,49,51,54,57,58,59,62,63,67,69,73,74,75,76,79,81,82,85,87,90,
%U A247635 92,94,97,98,106,114,115,116,117,121,123,124,125,126,128
%N A247635 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 A247635 Every positive integer lies in exactly one of the sequences A247635 and A247636.
%H A247635 Clark Kimberling, <a href="/A247635/b247635.txt">Table of n, a(n) for n = 1..1000</a>
%e A247635 r has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, ...
%e A247635 s has binary digits 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, ...
%e A247635 so that a(1) = 2 and a(2) = 8.
%t A247635 z = 200; r = FractionalPart[Sqrt[2]]; s = FractionalPart[Sqrt[8]];
%t A247635 u = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[r, 2, z]];
%t A247635 v = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[s, 2, z]];
%t A247635 t = Table[If[u[[n]] == v[[n]], 1, 0], {n, 1, z}];
%t A247635 Flatten[Position[t, 1]]  (* A247635 *)
%t A247635 Flatten[Position[t, 0]]  (* A247636 *)
%Y A247635 Cf. A247636, A247631, A247523.
%K A247635 nonn,easy,base
%O A247635 1,1
%A A247635 _Clark Kimberling_, Sep 23 2014