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Infinite audioactive word that shifts 1 place left under "Look and Say" method A, starting with a(0)=0.
1

%I #14 Jul 28 2015 11:33:10

%S 0,1,0,1,1,1,0,3,1,1,0,1,3,2,1,1,0,1,1,1,3,1,2,2,1,1,0,3,1,1,3,1,1,2,

%T 2,2,1,1,0,1,3,2,1,1,3,2,1,3,2,2,1,1,0,1,1,1,3,1,2,2,1,1,3,1,2,1,1,1,

%U 3,2,2,2,1,1,0,3,1,1,3,1,1,2,2,2,1,1,3,1,1,1,2,3,1,1,3,3,2,2,1,1,0,1,3,2,1

%N Infinite audioactive word that shifts 1 place left under "Look and Say" method A, starting with a(0)=0.

%C Positions of zero are given by A088206.

%C The sequence is obtained by starting with 0 and then successively appending the count (number of repetitions) and the value which is seen, term after term: "one zero, one one, one zero, three ones, one zero, ...". Otherwise said, the sequence is defined by "Start with 0 and append the result of "Look and Say" applied to the sequence". The "shifted left under Look and Say" property is thus an immediate consequence of the definition. A less trivial property is that there cannot be a number larger than 3 in this sequence. - _M. F. Hasler_, Jul 28 2015

%e The initial terms {0,1,0,1,1,1,0,3,1,1,0,...} are shifted 1 place left by saying: "one 0, one 1, one 0, three 1's, one 0, ...", which drops the leading 0 to give {1,0,1,1,1,0,3,1,1,0,...}.

%o (PARI) a=List(0);my(i=1);while(#a<200,listput(a,1);listput(a,a[i]);while(a[i++]==a[#a],a[#a-1]++));a \\ _M. F. Hasler_, Jul 28 2015

%Y Cf. A088206, A088203, A087282, A005150.

%K nonn

%O 0,8

%A _Paul D. Hanna_, Sep 22 2003