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A356682
The lexicographically earliest infinite squarefree sequence of nonnegative integers that starts with 2, 1.
6
2, 1, 0, 1, 2, 0, 1, 0, 2, 0, 1, 2, 0, 2, 1, 0, 1, 2, 0, 1, 0, 2, 0, 1, 2, 1, 0, 1, 2, 0, 1, 0, 2, 0, 3, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 3, 0, 1, 0, 3, 0, 2, 0, 1, 0, 2, 0, 3, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 3, 0, 1, 0, 3, 1, 0, 1, 2, 0, 1, 0, 2
OFFSET
1,1
LINKS
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 A356682
def A356682_list(n):
return build_square_free([2, 1], n)
print(A356682_list(87))
CROSSREFS
Other word starts: A007814 (w=0), A356677 (w=1), A356678 (w=2), A356679 (w=3), A356680 (w=1,2), A356681 (w=1,3), this sequence (w=2,1).
Sequence in context: A178651 A046810 A328515 * A323989 A262988 A039999
KEYWORD
nonn
AUTHOR
Joey Lakerdas-Gayle, Oct 18 2022
STATUS
approved