A247454 Numbers k such that d(r,k) = d(s,k), where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(3)}, and { } = fractional part.

3, 5, 6, 7, 9, 12, 16, 17, 19, 20, 22, 23, 24, 28, 29, 30, 32, 33, 37, 41, 45, 48, 49, 52, 56, 57, 58, 61, 62, 66, 67, 69, 74, 75, 76, 81, 82, 88, 89, 90, 91, 93, 96, 98, 99, 101, 102, 104, 105, 106, 108, 111, 113, 115, 116, 117, 120, 122, 125, 129, 130, 131

Offset

1,1

Comments

Every positive integer lies in exactly one of the sequences A247454 and A247324. Let s denote either sequence; is lim(#s < n)/n = 1/2, where (#s < n) represents the number of numbers in s that are < n?

Links

Clark Kimberling, Table of n, a(n) for n = 1..1000

Example

{sqrt(2)} has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1,...
{sqrt(3)} has binary digits 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0,..
so that a(1) = 3 and a(2) = 5.

Mathematica

z = 200; r = FractionalPart[Sqrt[2]]; s = FractionalPart[Sqrt[3]];
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]]  (* A247454 *)
Flatten[Position[t, 0]]  (* A247324 *)

Crossrefs

Cf. A246356, A247324.

Sequence in context: A043808 A043817 A030731 * A243912 A242883 A163621

Adjacent sequences: A247451 A247452 A247453 * A247455 A247456 A247457

Keyword

nonn,easy,base

Author

Clark Kimberling, Sep 17 2014

Status

approved