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Run lengths in infinite binary Champernowne string (A030190) formed by concatenation of 0, 1, 2 ... in base 2.
5

%I #27 Aug 12 2019 17:41:17

%S 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,

%T 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,

%U 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

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

%H Reinhard Zumkeller, <a href="/A056062/b056062.txt">Table of n, a(n) for n = 0..10000</a>

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

%t Length /@ (Split@(Join @@ Table[ IntegerDigits[i, 2], {i, 0, 100}])) (* _Olivier GĂ©rard_, Mar 27 2011 *)

%t Length/@Split[Flatten[IntegerDigits[Range[0,50],2]]] (* _Harvey P. Dale_, May 24 2015 *)

%o (Haskell)

%o import Data.List (group)

%o a056062 n = a056062_list !! n

%o a056062_list = map length $ group a030190_list

%o -- _Reinhard Zumkeller_, Mar 26 2013

%Y Cf. A030190, A003607, A030306, A318924.

%K easy,nonn,nice,base

%O 0,2

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

%E Edited by _Charles R Greathouse IV_, Apr 26 2010

%E Data corrected for n > 44 by _Reinhard Zumkeller_, Mar 26 2013