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A277157
Lexicographically least sequence of nonnegative integers that avoids 13/7-powers.
4
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0
OFFSET
0
COMMENTS
This sequence is 19-regular.
More generally, if a/b is a rational number in the interval 5/3 <= a/b < 2 with gcd(b, 2) = 1 and gcd(a, b) = 1, then the lexicographically least sequence of nonnegative integers that avoids a/b-powers is (2 a - b)-regular.
LINKS
Lara Pudwell and Eric Rowland, Avoiding fractional powers over the natural numbers, arXiv:1510.02807 [math.CO] (2015).
FORMULA
a(19 n + 18) = a(n) + 1.
MATHEMATICA
(* This gives the first 6859 terms. *)
SubstitutionSystem[{n_ :> {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, n + 1}}, {0}, {{3}}]
CROSSREFS
Cf. A277143, A277149, A277156 (sequences in the same family).
Sequence in context: A011727 A297042 A088918 * A277160 A277163 A011726
KEYWORD
nonn
AUTHOR
Eric Rowland, Oct 01 2016
STATUS
approved