A247547 Numbers k such that d(r,k) != d(s,k), where d(x,k) = k-th binary digit of x, r = {e}, s = {1/e}, and { } = fractional part.

1, 2, 3, 5, 8, 9, 10, 13, 14, 21, 24, 25, 27, 28, 29, 31, 35, 36, 37, 40, 42, 44, 48, 49, 50, 51, 52, 54, 56, 58, 59, 60, 70, 72, 73, 75, 77, 78, 79, 80, 81, 84, 85, 86, 87, 88, 95, 101, 102, 105, 107, 117, 119, 121, 122, 125, 127, 129, 131, 132, 133, 138

Offset

1,2

Comments

Every positive integer lies in exactly one of the sequences A247546 and A247547.

Links

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

Example

{e/1} has binary digits 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, ...
{1/e} has binary digits 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, ...
so that a(1) = 4 and a(2) = 6.

Mathematica

z = 200; r = FractionalPart[E]; s = FractionalPart[1/E];
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]]   (* A247546 *)
Flatten[Position[t, 0]]   (* A247547 *)

Crossrefs

Cf. A247546.

Sequence in context: A113051 A047372 A308469 * A096974 A286486 A285092

Adjacent sequences: A247544 A247545 A247546 * A247548 A247549 A247550

Keyword

nonn,easy,base

Author

Clark Kimberling, Sep 21 2014

Status

approved