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%I #21 Mar 16 2019 17:44:02
%S 1,1,2,2,1,2,1,1,2,1,1,2,2,1,2,2,1,1,2,1,2,2,1,2,1,1,2,2,1,2,2,1,2,1,
%T 1,2,1,1,2,2,1,2,1,1,2,1,2,2,1,2,2,1,1,2,1,1,2,2,1,2,1,1,2,1,1,2,2,1,
%U 2,2,1,2,1,1,2,1,2,2,1,1,2,1,1,2,2,1,2,1,1,2,1,1,2,2,1,2,2,1,1,2,1,2,2,1,2
%N Anti-Kolakoski sequence (sequence of run lengths never coincides with the sequence itself).
%C Unique infinite word defined on alphabet {1,2} satisfying: a(1)=1, if a(n)=2 length of n-th run is 1, if a(n)=1 length of n-th run is 2. Kolakoski sequence satisfies the opposite definition: K(1)=1, if K(n)=2 length of n-th run is 2, if K(n)=1 length of n-th run is 1.
%C Equals A049705 without the first term. - _Jean-Christophe Hervé_, Nov 10 2014
%F a(n) = 3 - A000002(n+1) = A049705(n+1).
%e a(1)=1 hence first run must have length 2 and necessarily a(2)=1. Now second run must also have length 2 and therefore a(3) = a(4) = 2.
%Y Cf. A000002, A049705.
%K nonn
%O 1,3
%A _Benoit Cloitre_, Nov 17 2003
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