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

0,4

Comments

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

Links

Table of n, a(n) for n=0..80.

Example

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].

Prog

(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))

Crossrefs

Cf. A006345, A157238, A283131, A007814.

Sequence in context: A171774 A002324 A101671 * A078979 A063974 A144628

Adjacent sequences: A333322 A333323 A333324 * A333326 A333327 A333328

Keyword

nonn

Author

Jan Koornstra, Mar 15 2020

Status

approved