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A247324 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. 2
1, 2, 4, 8, 10, 11, 13, 14, 15, 18, 21, 25, 26, 27, 31, 34, 35, 36, 38, 39, 40, 42, 43, 44, 46, 47, 50, 51, 53, 54, 55, 59, 60, 63, 64, 65, 68, 70, 71, 72, 73, 77, 78, 79, 80, 83, 84, 85, 86, 87, 92, 94, 95, 97, 100, 103, 107, 109, 110, 112, 114, 118, 119 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Every positive integer lies in exactly one of the sequences A247454 and A247324.

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) = 1 and a(2) = 2.

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, A247454.

Sequence in context: A319561 A153181 A256624 * A043706 A296691 A028836

Adjacent sequences:  A247321 A247322 A247323 * A247325 A247326 A247327

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Sep 17 2014

STATUS

approved

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Last modified November 12 09:25 EST 2019. Contains 329054 sequences. (Running on oeis4.)