A247633 Numbers k such that d(r,k) = 1 and d(s,k) = 0, where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(8)}, and { } = fractional part.

3, 5, 7, 13, 19, 23, 27, 36, 41, 46, 50, 53, 56, 61, 65, 68, 71, 77, 80, 84, 88, 91, 95, 99, 101, 103, 105, 108, 110, 112, 118, 120, 127, 133, 135, 138, 143, 146, 152, 156, 158, 160, 164, 167, 172, 176, 178, 180, 185, 189, 194, 197, 199, 203, 208, 210, 213

Offset

1,1

Comments

Every positive integer lies in exactly one of these: A247631, A247632, A247633, A247634.

Links

Clark Kimberling, Table of n, a(n) for n = 1..1096

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) = 4.

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. A247631, A247632, A247634.

Sequence in context: A075571 A077133 A164642 * A357170 A277717 A120460

Adjacent sequences: A247630 A247631 A247632 * A247634 A247635 A247636

Keyword

nonn,easy,base

Author

Clark Kimberling, Sep 23 2014

Status

approved