A247636 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(8)}, and { } = fractional part.

1, 3, 4, 5, 6, 7, 12, 13, 15, 19, 21, 23, 25, 27, 29, 36, 38, 41, 42, 46, 48, 50, 52, 53, 55, 56, 60, 61, 64, 65, 66, 68, 70, 71, 72, 77, 78, 80, 83, 84, 86, 88, 89, 91, 93, 95, 96, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 112, 113, 118

Offset

1,2

Comments

Every positive integer lies in exactly one of the sequences A247635 and A247636.

Links

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

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) = 1 and a(2) = 3.

Mathematica

z = 200; 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]];
t = Table[If[u[[n]] == v[[n]], 1, 0], {n, 1, z}];
Flatten[Position[t, 1]]  (* A247635 *)
Flatten[Position[t, 0]]  (* A247636 *)

Crossrefs

Cf. A247635, A247632, A247524.

Sequence in context: A210450 A133896 A052002 * A361267 A070916 A078305

Adjacent sequences: A247633 A247634 A247635 * A247637 A247638 A247639

Keyword

nonn,easy,base

Author

Clark Kimberling, Sep 23 2014

Status

approved