%I #12 Jan 03 2024 07:42:56

%S 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 44,45,47,49,51,54,57,58,59,62,63,67,69,73,74,75,76,79,81,82,85,87,90,

%U 92,94,97,98,106,114,115,116,117,121,123,124,125,126,128

%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="/A247635/b247635.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) = 2 and a(2) = 8.

%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. A247636, A247631, A247523.

%K nonn,easy,base

%O 1,1

%A _Clark Kimberling_, Sep 23 2014