A247459 Numbers k such that d(r,k) = d(s,k), where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {3*sqrt(2)}, and { } = fractional part.

1, 3, 5, 7, 8, 9, 10, 11, 13, 15, 16, 17, 19, 21, 23, 25, 27, 29, 30, 31, 32, 33, 34, 36, 38, 39, 40, 42, 43, 44, 46, 48, 50, 51, 53, 54, 56, 57, 58, 59, 61, 62, 64, 66, 68, 70, 72, 73, 74, 75, 76, 78, 80, 81, 82, 84, 86, 87, 89, 91, 93, 94, 96, 97, 99, 101

Offset

1,2

Comments

Every positive integer lies in exactly one of the sequences A247459 and A247460.

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) = 1 and a(2) = 3.

Mathematica

z = 200; 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]];
t = Table[If[u[[n]] == v[[n]], 1, 0], {n, 1, z}];
Flatten[Position[t, 1]]  (* A247459 *)
Flatten[Position[t, 0]]  (* A247460 *)

Crossrefs

Cf. A247460, A247455, A247454.

Sequence in context: A131903 A141114 A136443 * A020491 A168501 A173186

Adjacent sequences: A247456 A247457 A247458 * A247460 A247461 A247462

Keyword

nonn,easy,base

Author

Clark Kimberling, Sep 18 2014

Status

approved