A233836 Run lengths of ones and zeros in binary expansion of sqrt(2), cf. A004539.

1, 1, 2, 1, 1, 1, 1, 5, 1, 2, 4, 2, 2, 2, 2, 2, 7, 2, 3, 1, 4, 2, 2, 2, 1, 2, 1, 4, 1, 3, 1, 1, 2, 2, 1, 1, 5, 1, 2, 3, 1, 2, 2, 1, 2, 2, 2, 1, 3, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 5, 1, 1, 2, 5, 3, 3, 1, 1, 1, 2, 1, 4, 1, 2, 5, 1, 1, 3, 1, 1, 1, 1, 3

Offset: 1

Author

Reinhard Zumkeller, Dec 16 2013

Keywords

• nonn

Examples

			. A004539: 1 0 1 1 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 0 1 1 ...
.    runs: _ _ ___ _ _ _ _ _________ _ ___ _______ ___ ___ ___ ___ ...
. lengths: 1 1  2  1 1 1 1     5     1  2     4     2   2   2   2  ...
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A084186, A084187, A175911.

Programs

Haskell

import Data.List (group)
a233836 n = a233836_list !! (n-1)
a233836_list = map length $ group a004539_list

Mathematica

Length/@Split[RealDigits[Sqrt[2],2,300][[1]]] (* Harvey P. Dale, Oct 11 2020 *)