login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A247456 Numbers k such that d(r,k) = 0 and d(s,k) = 1, where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {3*sqrt(2)}, and { } = fractional part. 4
4, 6, 12, 14, 20, 24, 28, 37, 47, 52, 55, 60, 63, 69, 83, 85, 92, 100, 102, 104, 106, 119, 121, 129, 150, 157, 159, 163, 166, 168, 177, 179, 184, 186, 190, 198, 201, 215, 219, 228, 232, 236, 241, 246, 250, 252, 254, 256, 258, 271, 276, 284, 288, 303, 305 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Every positive integer lies in exactly one of these: A247455, A247456, A247457, A247458.

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) = 4 and a(2) = 6.

MATHEMATICA

z = 400; 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]]

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]]  (* A247455 *)

Flatten[Position[t2, 1]]  (* A247456 *)

Flatten[Position[t3, 1]]  (* A247457 *)

Flatten[Position[t4, 1]]  (* A247458 *)

CROSSREFS

Cf. A247455, A247457, A247458.

Sequence in context: A047406 A136415 A310596 * A266383 A217948 A059891

Adjacent sequences:  A247453 A247454 A247455 * A247457 A247458 A247459

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Sep 18 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 25 01:46 EST 2020. Contains 331229 sequences. (Running on oeis4.)