cp's OEIS Frontend

A247456 Numbers k such that d(r,k) = 0 and d(s,k) = 1, where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {3*sqrt(2)}, and { } = fractional part.

%I A247456 #14 Sep 28 2014 09:11:06
%S A247456 4,6,12,14,20,24,28,37,47,52,55,60,63,69,83,85,92,100,102,104,106,119,
%T A247456 121,129,150,157,159,163,166,168,177,179,184,186,190,198,201,215,219,
%U A247456 228,232,236,241,246,250,252,254,256,258,271,276,284,288,303,305
%N A247456 Numbers k such that d(r,k) = 0 and d(s,k) = 1, where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {3*sqrt(2)}, and { } = fractional part.
%C A247456 Every positive integer lies in exactly one of these: A247455, A247456, A247457, A247458.
%H A247456 Clark Kimberling, <a href="/A247456/b247456.txt">Table of n, a(n) for n = 1..500</a>
%e A247456 {1*sqrt(2)} has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1,...
%e A247456 {3*sqrt(2)} has binary digits 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1,...
%e A247456 so that a(1) = 4 and a(2) = 6.
%t A247456 z = 400; r = FractionalPart[Sqrt[2]]; s = FractionalPart[3*Sqrt[2]];
%t A247456 u = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[r, 2, z]]
%t A247456 v = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[s, 2, z]]
%t A247456 t1 = Table[If[u[[n]] == 0 && v[[n]] == 0, 1, 0], {n, 1, z}];
%t A247456 t2 = Table[If[u[[n]] == 0 && v[[n]] == 1, 1, 0], {n, 1, z}];
%t A247456 t3 = Table[If[u[[n]] == 1 && v[[n]] == 0, 1, 0], {n, 1, z}];
%t A247456 t4 = Table[If[u[[n]] == 1 && v[[n]] == 1, 1, 0], {n, 1, z}];
%t A247456 Flatten[Position[t1, 1]]  (* A247455 *)
%t A247456 Flatten[Position[t2, 1]]  (* A247456 *)
%t A247456 Flatten[Position[t3, 1]]  (* A247457 *)
%t A247456 Flatten[Position[t4, 1]]  (* A247458 *)
%Y A247456 Cf. A247455, A247457, A247458.
%K A247456 nonn,easy,base
%O A247456 1,1
%A A247456 _Clark Kimberling_, Sep 18 2014