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A247634 Numbers k such that d(r,k) = 1 and d(s,k) = 1, where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(8)}, and { } = fractional part.

%I A247634 #10 Sep 26 2014 21:14:27
%S A247634 2,16,17,18,22,26,30,31,32,33,34,35,39,40,43,44,45,49,67,73,74,75,76,
%T A247634 79,87,90,94,97,98,114,115,116,117,123,124,125,126,131,132,137,140,
%U A247634 141,142,145,154,155,170,171,174,175,188,192,193,196,205,206,207,212
%N A247634 Numbers k such that d(r,k) = 1 and d(s,k) = 1, where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(8)}, and { } = fractional part.
%C A247634 Every positive integer lies in exactly one of these: A247631, A247632, A247633, A247634.
%H A247634 Clark Kimberling, <a href="/A247634/b247634.txt">Table of n, a(n) for n = 1..1122</a>
%e A247634 r has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, ...
%e A247634 s has binary digits 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, ...
%e A247634 so that a(1) = 1 and a(2) = 4.
%t A247634 z = 400; r = FractionalPart[Sqrt[2]]; s = FractionalPart[Sqrt[8]];
%t A247634 u = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[r, 2, z]]
%t A247634 v = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[s, 2, z]]
%t A247634 t1 = Table[If[u[[n]] == 0 && v[[n]] == 0, 1, 0], {n, 1, z}];
%t A247634 t2 = Table[If[u[[n]] == 0 && v[[n]] == 1, 1, 0], {n, 1, z}];
%t A247634 t3 = Table[If[u[[n]] == 1 && v[[n]] == 0, 1, 0], {n, 1, z}];
%t A247634 t4 = Table[If[u[[n]] == 1 && v[[n]] == 1, 1, 0], {n, 1, z}];
%t A247634 Flatten[Position[t1, 1]]  (* A247631 *)
%t A247634 Flatten[Position[t2, 1]]  (* A247632 *)
%t A247634 Flatten[Position[t3, 1]]  (* A247633 *)
%t A247634 Flatten[Position[t4, 1]]  (* A247634 *)
%Y A247634 Cf. A247631, A247632, A247633.
%K A247634 nonn,easy,base
%O A247634 1,1
%A A247634 _Clark Kimberling_, Sep 23 2014