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Run lengths of ones and zeros in binary expansion of sqrt(2), cf. A004539.
5

%I #6 Oct 11 2020 15:49:34

%S 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,

%T 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,

%U 3,1,1,1,2,1,4,1,2,5,1,1,3,1,1,1,1,3

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

%H Reinhard Zumkeller, <a href="/A233836/b233836.txt">Table of n, a(n) for n = 1..10000</a>

%e . 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 ...

%e . runs: _ _ ___ _ _ _ _ _________ _ ___ _______ ___ ___ ___ ___ ...

%e . lengths: 1 1 2 1 1 1 1 5 1 2 4 2 2 2 2 ...

%t Length/@Split[RealDigits[Sqrt[2],2,300][[1]]] (* _Harvey P. Dale_, Oct 11 2020 *)

%o (Haskell)

%o import Data.List (group)

%o a233836 n = a233836_list !! (n-1)

%o a233836_list = map length $ group a004539_list

%Y Cf. A084186, A084187, A175911.

%K nonn

%O 1,3

%A _Reinhard Zumkeller_, Dec 16 2013