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!)
A247521 Numbers k such that d(r,k) = 1 and d(s,k) = 0, where d(x,k) = k-th binary digit of x, r = {golden ratio}, s = {(golden ratio)/2}, and { } = fractional part. 4
4, 11, 14, 18, 24, 27, 32, 34, 42, 45, 47, 50, 60, 62, 64, 71, 76, 81, 90, 98, 100, 105, 109, 112, 117, 123, 126, 132, 137, 143, 147, 150, 154, 157, 159, 167, 171, 175, 178, 183, 186, 188, 192, 202, 205, 210, 213, 215, 220, 224, 228, 233, 240, 245, 249, 252 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Every positive integer lies in exactly one of these: A247519, A247520, A247522.

LINKS

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

EXAMPLE

r has binary digits 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, ...

s has binary digits 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, ...

so that a(1) = 4.

MATHEMATICA

z = 400; r1 = GoldenRatio; r = FractionalPart[r1]; s = FractionalPart[r1/2];

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]] (* A247519 *)

Flatten[Position[t2, 1]] (* A247520 *)

Flatten[Position[t3, 1]] (* A247521 *)

Flatten[Position[t4, 1]] (* A247522 *)

CROSSREFS

Cf. A247519, A247520, A247522.

Sequence in context: A095797 A205846 A204542 * A285979 A299975 A271508

Adjacent sequences:  A247518 A247519 A247520 * A247522 A247523 A247524

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Sep 19 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 February 18 09:15 EST 2020. Contains 332011 sequences. (Running on oeis4.)