A247631 Numbers k such that d(r,k) = 0 and d(s,k) = 0, where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(8)}, and { } = fractional part.

8, 9, 10, 11, 14, 20, 24, 28, 37, 47, 51, 54, 57, 58, 59, 62, 63, 69, 81, 82, 85, 92, 106, 121, 128, 129, 147, 148, 149, 150, 161, 162, 165, 168, 181, 182, 183, 186, 190, 200, 201, 214, 217, 218, 219, 225, 226, 227, 228, 232, 236, 241, 245, 248, 249, 258

Offset

1,1

Comments

Every positive integer lies in exactly one of these: A247631, A247632, A247633, A247634. Deleting the initial 1 from the representation of r gives the representation of s.

Links

Clark Kimberling, Table of n, a(n) for n = 1..1181

Example

r has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, ...
s has binary digits 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, ...
so that a(1) = 8 and a(2) = 9.

Mathematica

z = 400; r = FractionalPart[Sqrt[2]]; s = FractionalPart[Sqrt[8]];
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]]  (* A247631 *)
Flatten[Position[t2, 1]]  (* A247632 *)
Flatten[Position[t3, 1]]  (* A247633 *)
Flatten[Position[t4, 1]]  (* A247634 *)

Crossrefs

Cf. A247632, A247633, A247634, A247519.

Sequence in context: A067729 A058366 A120209 * A297260 A296701 A297134

Adjacent sequences: A247628 A247629 A247630 * A247632 A247633 A247634

Keyword

nonn,easy,base

Author

Clark Kimberling, Sep 23 2014

Status

approved