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A247631 Numbers k such that d(r,k) = 0 and d(s,k) = 0, where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(8)}, and { } = fractional part. 5
8, 9, 10, 11, 14, 20, 24, 28, 37, 47, 51, 54, 57, 58, 59, 62, 63, 69, 81, 82, 85, 92, 106, 121, 128, 129, 147, 148, 149, 150, 161, 162, 165, 168, 181, 182, 183, 186, 190, 200, 201, 214, 217, 218, 219, 225, 226, 227, 228, 232, 236, 241, 245, 248, 249, 258 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Every positive integer lies in exactly one of these: A247631, A247632, A247633, A247634.  Deleting the initial 1 from the representation of r gives the representation of s.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1181

EXAMPLE

r has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, ...

s has binary digits 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, ...

so that a(1) = 8 and a(2) = 9.

MATHEMATICA

z = 400; r = FractionalPart[Sqrt[2]]; s = FractionalPart[Sqrt[8]];

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]]  (* A247631 *)

Flatten[Position[t2, 1]]  (* A247632 *)

Flatten[Position[t3, 1]]  (* A247633 *)

Flatten[Position[t4, 1]]  (* A247634 *)

CROSSREFS

Cf. A247632, A247633, A247634, A247519.

Sequence in context: A067729 A058366 A120209 * A297260 A296701 A297134

Adjacent sequences:  A247628 A247629 A247630 * A247632 A247633 A247634

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Sep 23 2014

STATUS

approved

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Last modified February 21 15:11 EST 2019. Contains 320374 sequences. (Running on oeis4.)