A247458 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 = {3*sqrt(2)}, and { } = fractional part.

3, 5, 7, 13, 16, 17, 19, 23, 27, 30, 31, 32, 33, 34, 36, 39, 40, 43, 44, 46, 50, 53, 56, 61, 68, 73, 74, 75, 76, 80, 84, 87, 91, 94, 97, 99, 101, 103, 105, 114, 115, 116, 118, 120, 123, 124, 125, 127, 131, 132, 137, 140, 141, 142, 146, 154, 156, 158, 160

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..1000

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) = 3 and a(2) = 5.

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, A247456, A247457.

Sequence in context: A192110 A246026 A188574 * A355424 A339501 A008996

Adjacent sequences: A247455 A247456 A247457 * A247459 A247460 A247461

Keyword

nonn,easy,base

Author

Clark Kimberling, Sep 18 2014

Status

approved