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A247545 Numbers k such that d(r,k) = 1 and d(s,k) = 1, where d(x,k) = k-th binary digit of x, r = {e}, s = {1/e}, and { } = fractional part. 4
4, 6, 7, 11, 16, 18, 20, 26, 33, 39, 41, 43, 45, 46, 53, 55, 61, 63, 65, 67, 68, 69, 71, 74, 76, 82, 89, 97, 100, 106, 108, 110, 113, 114, 115, 116, 120, 126, 128, 130, 135, 137, 150, 157, 159, 163, 164, 171, 174, 178, 180, 183, 188, 191, 195, 206, 209, 212 (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
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 = 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
Sequence in context: A022436 A102139 A167228 * A310655 A102145 A102132
KEYWORD
nonn,easy,base
AUTHOR
Clark Kimberling, Sep 21 2014
STATUS
approved

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Last modified June 15 22:50 EDT 2024. Contains 373412 sequences. (Running on oeis4.)