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A247544 Numbers k such that d(r,k) = 1 and d(s,k) = 0, where d(x,k) = k-th binary digit of x, r = {e}, s = {1/e}, and { } = fractional part. 4
1, 3, 8, 9, 10, 24, 27, 31, 37, 42, 48, 51, 58, 59, 70, 72, 75, 80, 84, 85, 101, 102, 105, 107, 119, 121, 122, 127, 131, 138, 139, 142, 143, 144, 148, 151, 158, 160, 165, 169, 172, 177, 181, 186, 190, 193, 198, 199, 200, 201, 210, 222, 226, 228, 233, 236 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Every positive integer lies in exactly one of these: A247542, A247543, A247544, A247545.

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) = 2 and a(2) = 5.

MATHEMATICA

z = 400; 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]]

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]]  (* A247542 *)

Flatten[Position[t2, 1]]  (* A247543 *)

Flatten[Position[t3, 1]]  (* A247544 *)

Flatten[Position[t4, 1]]  (* A247545 *)

CROSSREFS

Cf. A247542, A247543, A247545.

Sequence in context: A051208 A211223 A350776 * A080524 A024550 A173179

Adjacent sequences:  A247541 A247542 A247543 * A247545 A247546 A247547

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Sep 21 2014

STATUS

approved

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Last modified January 28 15:20 EST 2022. Contains 350657 sequences. (Running on oeis4.)