A247632 Numbers k such that d(r,k) = 0 and d(s,k) = 1, where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(8)}, and { } = fractional part.

1, 4, 6, 12, 15, 21, 25, 29, 38, 42, 48, 52, 55, 60, 64, 66, 70, 72, 78, 83, 86, 89, 93, 96, 100, 102, 104, 107, 109, 111, 113, 119, 122, 130, 134, 136, 139, 144, 151, 153, 157, 159, 163, 166, 169, 173, 177, 179, 184, 187, 191, 195, 198, 202, 204, 209, 211

Offset

1,2

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..1097

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, A247633, A247634.

Sequence in context: A251630 A256241 A364385 * A104236 A265225 A122781

Adjacent sequences: A247629 A247630 A247631 * A247633 A247634 A247635

Keyword

nonn,easy,base

Author

Clark Kimberling, Sep 23 2014

Status

approved