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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.
2
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
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
KEYWORD
nonn,easy,base
AUTHOR
Clark Kimberling, Sep 21 2014
STATUS
approved