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A247633 Numbers k such that d(r,k) = 1 and d(s,k) = 0, where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(8)}, and { } = fractional part.

%I A247633 #10 Sep 26 2014 21:14:41
%S A247633 3,5,7,13,19,23,27,36,41,46,50,53,56,61,65,68,71,77,80,84,88,91,95,99,
%T A247633 101,103,105,108,110,112,118,120,127,133,135,138,143,146,152,156,158,
%U A247633 160,164,167,172,176,178,180,185,189,194,197,199,203,208,210,213
%N A247633 Numbers k such that d(r,k) = 1 and d(s,k) = 0, where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(8)}, and { } = fractional part.
%C A247633 Every positive integer lies in exactly one of these: A247631, A247632, A247633, A247634.
%H A247633 Clark Kimberling, <a href="/A247633/b247633.txt">Table of n, a(n) for n = 1..1096</a>
%e A247633 r has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, ...
%e A247633 s has binary digits 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, ...
%e A247633 so that a(1) = 1 and a(2) = 4.
%t A247633 z = 400; r = FractionalPart[Sqrt[2]]; s = FractionalPart[Sqrt[8]];
%t A247633 u = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[r, 2, z]]
%t A247633 v = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[s, 2, z]]
%t A247633 t1 = Table[If[u[[n]] == 0 && v[[n]] == 0, 1, 0], {n, 1, z}];
%t A247633 t2 = Table[If[u[[n]] == 0 && v[[n]] == 1, 1, 0], {n, 1, z}];
%t A247633 t3 = Table[If[u[[n]] == 1 && v[[n]] == 0, 1, 0], {n, 1, z}];
%t A247633 t4 = Table[If[u[[n]] == 1 && v[[n]] == 1, 1, 0], {n, 1, z}];
%t A247633 Flatten[Position[t1, 1]]  (* A247631 *)
%t A247633 Flatten[Position[t2, 1]]  (* A247632 *)
%t A247633 Flatten[Position[t3, 1]]  (* A247633 *)
%t A247633 Flatten[Position[t4, 1]]  (* A247634 *)
%Y A247633 Cf. A247631, A247632, A247634.
%K A247633 nonn,easy,base
%O A247633 1,1
%A A247633 _Clark Kimberling_, Sep 23 2014