A333325 Lexicographically earliest sequence over {0,1,2} that has the shortest square subsequence.

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, 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, 0, 1, 2, 0, 2, 2, 0, 1, 0, 2, 0, 1, 2

Offset: 0

Author

Jan Koornstra, Mar 15 2020

Keywords

• nonn

Comments

This is very similar to A333307. See that sequence for details about the precise definition. - N. J. A. Sloane, Nov 29 2020

Examples

			a(7) = 0, since:
0 yields a square subsequence of length 2: [0, 0],
1 of length 4: [0, 1, 0, 1],
2 of length 8: [0, 1, 0, 2, 0, 1, 0, 2].
		

Crossrefs

Cf. A006345, A157238, A283131, A007814.

Programs

Python

def a333325(n):
  seq = []
  for k in range(n):
    options = []
    l = len(seq) + 1
    for m in range(3): # base
      for i in range(l // 2, -1, -1):
        if seq[l - 2 * i: l - i] == seq[l - i:] + [m]: break
      options.append(2 * i)
    seq.append(options.index(min(options)))
  return seq
print(a333325(81))