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A247454 Numbers k such that d(r,k) = d(s,k), where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(3)}, and { } = fractional part. 8
3, 5, 6, 7, 9, 12, 16, 17, 19, 20, 22, 23, 24, 28, 29, 30, 32, 33, 37, 41, 45, 48, 49, 52, 56, 57, 58, 61, 62, 66, 67, 69, 74, 75, 76, 81, 82, 88, 89, 90, 91, 93, 96, 98, 99, 101, 102, 104, 105, 106, 108, 111, 113, 115, 116, 117, 120, 122, 125, 129, 130, 131 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Every positive integer lies in exactly one of the sequences A247454 and A247324.  Let s denote either sequence; is lim(#s < n)/n = 1/2, 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) = 3 and a(2) = 5.

MATHEMATICA

z = 200; 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]];

t = Table[If[u[[n]] == v[[n]], 1, 0], {n, 1, z}];

Flatten[Position[t, 1]]  (* A247454 *)

Flatten[Position[t, 0]]  (* A247324 *)

CROSSREFS

Cf. A246356, A247324.

Sequence in context: A043808 A043817 A030731 * A243912 A242883 A163621

Adjacent sequences:  A247451 A247452 A247453 * A247455 A247456 A247457

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Sep 17 2014

STATUS

approved

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Last modified January 19 20:41 EST 2020. Contains 331066 sequences. (Running on oeis4.)