login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A076478 The binary Champernowne sequence: concatenate binary vectors of lengths 1, 2, 3, ... in numerical order. 15
0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Can also be seen as triangle where row n contains all binary vectors of length n+1. - Reinhard Zumkeller, Aug 18 2015

REFERENCES

Bodil Branner, Dynamics, Chap. IV.14 of The Princeton Companion to Mathematics, ed. T. Gowers, p. 499.

K. Dajani and C. Kraaikamp, Ergodic Theory of Numbers, Math. Assoc. America, 2002, p. 72.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Michael Barnsley, and Andrew Vince, Self-similar polygonal tiling, The American Mathematical Monthly 124.10 (2017): 905-921. See page 917.

Igor Pak, Complexity problems in enumerative combinatorics, arXiv:1803.06636 [math.CO], 2018.

FORMULA

To get the m-th binary vector, write m+1 in base 2 and remove the initial 1. - Clark Kimberling, Feb 07 2010

EXAMPLE

0,

1,

0,0,

0,1,

1,0,

1,1,

0,0,0,

0,0,1,

0,1,0,

0,1,1,

1,0,0,

1,0,1,

...

MATHEMATICA

d[n_] := Rest@IntegerDigits[n + 1, 2] + 1; -1 + Flatten[Array[d, 50]] (* Clark Kimberling, Feb 07 2012 *)

PROG

(PARI) {m=5; for(d=1, m, for(k=0, 2^d-1, v=binary(k); while(matsize(v)[2]<d, v=concat(0, v)); for(j=1, matsize(v)[2], print1(v[j], ", "))))}

(Haskell)

import Data.List (unfoldr)

a076478 n = a076478_list !! n

a076478_list = concat $ tail $ map (tail . reverse . unfoldr

   (\x -> if x == 0 then Nothing else Just $ swap $ divMod x 2 )) [1..]

-- Reinhard Zumkeller, Feb 08 2012

(Haskell)

a076478_row n = a076478_tabf !! n :: [[Int]]

a076478_tabf = tail $ iterate (\bs -> map (0 :) bs ++ map (1 :) bs) [[]]

a076478_list' = concat $ concat a076478_tabf

-- Reinhard Zumkeller, Aug 18 2015

CROSSREFS

Cf. A007931, A030308, A053645.

Sequence in context: A285831 A188294 A079101 * A091444 A091447 A106701

Adjacent sequences:  A076475 A076476 A076477 * A076479 A076480 A076481

KEYWORD

nonn,easy,tabf

AUTHOR

N. J. A. Sloane, Nov 10 2002

EXTENSIONS

Extended by Klaus Brockhaus, Nov 11 2002

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 March 23 16:52 EDT 2019. Contains 321432 sequences. (Running on oeis4.)