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A277155
Lexicographically least sequence of nonnegative integers that avoids 11/7-powers.
2
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0
OFFSET
0
COMMENTS
This sequence is 27-regular.
More generally, if a/b is a rational number in the interval 3/2 < a/b < 5/3 with gcd(b, 5) = 1 and gcd(a, b) = 1, then the lexicographically least sequence of nonnegative integers that avoids a/b-powers is (5 a - 4 b)-regular.
LINKS
Lara Pudwell and Eric Rowland, Avoiding fractional powers over the natural numbers, arXiv:1510.02807 [math.CO] (2015).
FORMULA
a(27 n + 26) = a(n) + 1.
MATHEMATICA
(* This gives the first 19683 terms. *)
SubstitutionSystem[{n_ :> {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, n + 1}}, {0}, {{3}}]
CROSSREFS
Cf. A277160 (sequence in the same family).
Sequence in context: A044941 A368699 A277151 * A277159 A011724 A037807
KEYWORD
nonn
AUTHOR
Eric Rowland, Oct 01 2016
STATUS
approved