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A356680
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The lexicographically earliest infinite squarefree sequence of nonnegative integers that starts with 1, 2.
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6
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1, 2, 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, 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, 0, 2, 0, 1, 2, 0, 2, 1
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OFFSET
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1,2
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LINKS
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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.
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PROG
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(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 A356680
return build_square_free([1, 2], n)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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