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A246356 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(3)}, and { } = fractional part. 7
6, 9, 12, 20, 24, 28, 29, 37, 48, 52, 57, 58, 62, 66, 69, 81, 82, 89, 93, 96, 102, 104, 106, 111, 113, 122, 129, 130, 139, 144, 149, 151, 159, 161, 163, 165, 166, 177, 179, 181, 186, 187, 190, 191, 195, 201, 202, 204, 217, 219, 220, 222, 225, 228, 232, 233 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Every positive integer lies in exactly one of these: A246356, A246357, A246358, A247356.  Let s denote any of these; is lim(#s < n)/n = 1/4, where (#s < n) represents the number of numbers in s that are < n?

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000

EXAMPLE

{sqrt(2)} has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1,...

{sqrt(3)} has binary digits 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0,..

so that a(1) = 6.

MATHEMATICA

z = 500; r = FractionalPart[Sqrt[2]]; s = FractionalPart[Sqrt[3]];

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]]  (* A246356 *)

Flatten[Position[t2, 1]]  (* A246357 *)

Flatten[Position[t3, 1]]  (* A246358 *)

Flatten[Position[t4, 1]]  (* A247356 *)

CROSSREFS

Cf. A247454, A246357, A246358, A247356.

Sequence in context: A036999 A290130 A118782 * A315960 A106218 A315961

Adjacent sequences:  A246353 A246354 A246355 * A246357 A246358 A246359

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Sep 17 2014

STATUS

approved

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Last modified January 24 01:05 EST 2020. Contains 331178 sequences. (Running on oeis4.)