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A247542 Numbers k such that d(r,k) = 0 and d(s,k) = 0, where d(x,k) = k-th binary digit of x, r = {e}, s = {1/e}, and { } = fractional part. 4
12, 15, 17, 19, 22, 23, 30, 32, 34, 38, 47, 57, 62, 64, 66, 83, 90, 91, 92, 93, 94, 96, 98, 99, 103, 104, 109, 111, 112, 118, 123, 124, 134, 136, 145, 146, 147, 149, 154, 156, 162, 167, 175, 176, 185, 189, 194, 197, 202, 204, 205, 207, 208, 214, 215, 219 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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) = 12 and a(2) = 15.

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. A247543, A247544, A247545.

Sequence in context: A260462 A114443 A188766 * A281880 A153047 A265128

Adjacent sequences:  A247539 A247540 A247541 * A247543 A247544 A247545

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Sep 21 2014

STATUS

approved

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Last modified December 7 09:15 EST 2021. Contains 349574 sequences. (Running on oeis4.)