A247546 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.

4, 6, 7, 11, 12, 15, 16, 17, 18, 19, 20, 22, 23, 26, 30, 32, 33, 34, 38, 39, 41, 43, 45, 46, 47, 53, 55, 57, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 74, 76, 82, 83, 89, 90, 91, 92, 93, 94, 96, 97, 98, 99, 100, 103, 104, 106, 108, 109, 110, 111, 112, 113, 114

Offset

1,1

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. A247547.

Sequence in context: A103057 A039590 A134038 * A110605 A206775 A287157

Adjacent sequences: A247543 A247544 A247545 * A247547 A247548 A247549

Keyword

nonn,easy,base

Author

Clark Kimberling, Sep 21 2014

Status

approved