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%I #21 Nov 29 2020 12:46:01
%S 0,1,0,2,0,1,0,0,1,2,0,1,0,2,0,1,2,0,2,1,0,1,2,0,1,0,2,0,1,2,0,2,2,0,
%T 1,0,2,0,1,2,0,0,1,0,2,0,1,0,0,1,2,0,1,0,2,0,1,2,0,2,1,0,1,2,0,1,0,2,
%U 0,1,2,0,2,2,0,1,0,2,0,1,2
%N Lexicographically earliest sequence over {0,1,2} that has the shortest square subsequence.
%C This is very similar to A333307. See that sequence for details about the precise definition. - _N. J. A. Sloane_, Nov 29 2020
%e a(7) = 0, since:
%e 0 yields a square subsequence of length 2: [0, 0],
%e 1 of length 4: [0, 1, 0, 1],
%e 2 of length 8: [0, 1, 0, 2, 0, 1, 0, 2].
%o (Python)
%o def a333325(n):
%o seq = []
%o for k in range(n):
%o options = []
%o l = len(seq) + 1
%o for m in range(3): # base
%o for i in range(l // 2, -1, -1):
%o if seq[l - 2 * i: l - i] == seq[l - i:] + [m]: break
%o options.append(2 * i)
%o seq.append(options.index(min(options)))
%o return seq
%o print(a333325(81))
%Y Cf. A006345, A157238, A283131, A007814.
%K nonn
%O 0,4
%A _Jan Koornstra_, Mar 15 2020
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