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.

4, 6, 12, 14, 20, 24, 28, 37, 47, 52, 55, 60, 63, 69, 83, 85, 92, 100, 102, 104, 106, 119, 121, 129, 150, 157, 159, 163, 166, 168, 177, 179, 184, 186, 190, 198, 201, 215, 219, 228, 232, 236, 241, 246, 250, 252, 254, 256, 258, 271, 276, 284, 288, 303, 305

Offset

1,1

Comments

Every positive integer lies in exactly one of these: A247455, A247456, A247457, A247458.

Links

Clark Kimberling, Table of n, a(n) for n = 1..500

Example

{1*sqrt(2)} has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1,...
{3*sqrt(2)} has binary digits 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1,...
so that a(1) = 4 and a(2) = 6.

Mathematica

z = 400; r = FractionalPart[Sqrt[2]]; s = FractionalPart[3*Sqrt[2]];
u = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[r, 2, z]]
v = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[s, 2, z]]
t1 = Table[If[u[[n]] == 0 && v[[n]] == 0, 1, 0], {n, 1, z}];
t2 = Table[If[u[[n]] == 0 && v[[n]] == 1, 1, 0], {n, 1, z}];
t3 = Table[If[u[[n]] == 1 && v[[n]] == 0, 1, 0], {n, 1, z}];
t4 = Table[If[u[[n]] == 1 && v[[n]] == 1, 1, 0], {n, 1, z}];
Flatten[Position[t1, 1]]  (* A247455 *)
Flatten[Position[t2, 1]]  (* A247456 *)
Flatten[Position[t3, 1]]  (* A247457 *)
Flatten[Position[t4, 1]]  (* A247458 *)

Crossrefs

Cf. A247455, A247457, A247458.

Sequence in context: A047406 A136415 A310596 * A266383 A217948 A059891

Adjacent sequences: A247453 A247454 A247455 * A247457 A247458 A247459

Keyword

nonn,easy,base

Author

Clark Kimberling, Sep 18 2014

Status

approved