A356681 The lexicographically earliest infinite squarefree sequence of nonnegative integers that starts with 1, 3.

1, 3, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 2, 0, 2, 1, 0, 1, 2, 0, 1, 0, 2, 0, 1, 2, 0, 2, 1, 0, 1, 3, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 2, 0, 2, 1, 0, 1, 2, 0, 1, 0, 2, 0, 1, 2, 0, 2, 1, 2, 0, 1, 0, 2, 0, 1, 2, 0, 3, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1

Offset

1,2

Links

Joey Lakerdas-Gayle, Table of n, a(n) for n = 1..10000

Siddharth Berera, Andrés Gómez-Colunga, Joey Lakerdas-Gayle, John López, Mauditra Matin, Daniel Roebuck, Eric Rowland, Noam Scully, and Juliet Whidden, The lexicographically least square-free word with a given prefix, arXiv:2210.00508 [math.CO], 2022.

Prog

(Python)
# check if appending letter to the end of word introduces a square
def makes_square(word, letter):
    new_word = word+[letter]
    for l in range(1, len(new_word) // 2 + 1):
        if new_word[-l:] == new_word[-2*l:-l]:
            return True
    return False
# returns a list of the first n letters of L(word)
def build_square_free(word, n):
    new_word = word[:]
    for i in range(n-len(word)):
        next_letter = 0
        while makes_square(new_word, next_letter):
            next_letter += 1
        new_word += [next_letter]
    return new_word
# returns a list of the first n terms of A356681
def A356681_list(n):
    return build_square_free([1, 3], n)
print(A356681_list(87))

Crossrefs

Other word starts: A007814 (w=0), A356677 (w=1), A356678 (w=2), A356679 (w=3), A356680 (w=1,2), this sequence (w=1,3), A356682 (w=2,1).

Sequence in context: A341716 A216600 A356679 * A093684 A101270 A351097

Adjacent sequences: A356678 A356679 A356680 * A356682 A356683 A356684

Keyword

nonn

Author

Joey Lakerdas-Gayle, Oct 18 2022

Status

approved