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A277160 Lexicographically least sequence of nonnegative integers that avoids 13/8-powers. 2
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
0
COMMENTS
This sequence is 33-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(33 n + 32) = a(n) + 1.
MATHEMATICA
(* This gives the first 35937 terms. *)
SubstitutionSystem[{n_ :> {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, n + 1}}, {0}, {{3}}]
CROSSREFS
Cf. A277155 (sequence in the same family).
Sequence in context: A297042 A088918 A277157 * A277163 A011726 A297041
KEYWORD
nonn
AUTHOR
Eric Rowland, Oct 01 2016
STATUS
approved

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Last modified June 14 03:16 EDT 2024. Contains 373392 sequences. (Running on oeis4.)