A056062 - OEIS

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

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OFFSET

0,2

LINKS

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

EXAMPLE

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

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 *)

PROG

(Haskell)