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A247460 Numbers k such that d(r,k) != d(s,k), where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {3*sqrt(2)}, and { } = fractional part. 2
2, 4, 6, 12, 14, 18, 20, 22, 24, 26, 28, 35, 37, 41, 45, 47, 49, 52, 55, 60, 63, 65, 67, 69, 71, 77, 79, 83, 85, 88, 90, 92, 95, 98, 100, 102, 104, 106, 108, 110, 112, 117, 119, 121, 126, 129, 133, 135, 138, 143, 145, 150, 152, 155, 157, 159, 163, 166, 168 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Every positive integer lies in exactly one of the sequences A247459 and A247460.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..500

EXAMPLE

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

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

so that a(1) = 2 and a(2) = 4.

MATHEMATICA

z = 200; r = FractionalPart[Sqrt[2]]; s = FractionalPart[3*Sqrt[2]];

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]]  (* A247459 *)

Flatten[Position[t, 0]]  (* A247460 *)

CROSSREFS

Cf. A247459, A247455, A247454.

Sequence in context: A271822 A067874 A015733 * A023187 A061012 A331620

Adjacent sequences:  A247457 A247458 A247459 * A247461 A247462 A247463

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Sep 18 2014

STATUS

approved

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Last modified February 25 08:42 EST 2020. Contains 332221 sequences. (Running on oeis4.)