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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. 2

%I

%S 4,6,7,11,12,15,16,17,18,19,20,22,23,26,30,32,33,34,38,39,41,43,45,46,

%T 47,53,55,57,61,62,63,64,65,66,67,68,69,71,74,76,82,83,89,90,91,92,93,

%U 94,96,97,98,99,100,103,104,106,108,109,110,111,112,113,114

%N 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.

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

%H Clark Kimberling, <a href="/A247546/b247546.txt">Table of n, a(n) for n = 1..1000</a>

%e {e/1} has binary digits 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, ...

%e {1/e} has binary digits 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, ...

%e so that a(1) = 4 and a(2) = 6.

%t z = 200; r = FractionalPart[E]; s = FractionalPart[1/E];

%t u = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[r, 2, z]];

%t v = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[s, 2, z]];

%t t = Table[If[u[[n]] == v[[n]], 1, 0], {n, 1, z}];

%t Flatten[Position[t, 1]] (* A247546 *)

%t Flatten[Position[t, 0]] (* A247547 *)

%Y Cf. A247547.

%K nonn,easy,base

%O 1,1

%A _Clark Kimberling_, Sep 21 2014

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Last modified January 24 18:41 EST 2022. Contains 350565 sequences. (Running on oeis4.)