A056062 Run lengths in infinite binary Champernowne string (A030190) formed by concatenation of 0, 1, 2 ... in base 2.

1, 2, 1, 3, 2, 1, 1, 3, 1, 4, 3, 1, 2, 2, 1, 1, 1, 1, 1, 4, 2, 2, 1, 4, 1, 5, 4, 1, 3, 2, 2, 1, 1, 1, 2, 3, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 5, 3, 2, 2, 3, 1, 1, 1, 2, 1, 5, 2, 3, 1, 5, 1, 6, 5, 1, 4, 2, 3, 1, 1, 1, 3, 3, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 4, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 0

Author

Helge Robitzsch (hrobi(AT)math.uni-goettingen.de), Jul 27 2000

Keywords

• easy
• nonn
• nice
• base

Examples

			The string starts with 011011100101110111... (concatenation of 0, 1, 10, 11, 100, 101, 110, 111, ...) so initial runs are 1, 2, 1, 3, ...
		

Links

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

Crossrefs

Cf. A030190, A003607, A030306, A318924.

Programs

Haskell

import Data.List (group)
a056062 n = a056062_list !! n
a056062_list = map length $ group a030190_list
-- Reinhard Zumkeller, Mar 26 2013

Mathematica

Length /@ (Split@(Join @@ Table[ IntegerDigits[i, 2], {i, 0, 100}]))  (*  Olivier Gérard, Mar 27 2011 *)
Length/@Split[Flatten[IntegerDigits[Range[0,50],2]]] (* Harvey P. Dale, May 24 2015 *)

Extensions

Edited by Charles R Greathouse IV, Apr 26 2010

Data corrected for n > 44 by Reinhard Zumkeller, Mar 26 2013