A277160 Lexicographically least sequence of nonnegative integers that avoids 13/8-powers.

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

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

Eric Rowland, Table of n, a(n) for n = 0..20000

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

Adjacent sequences: A277157 A277158 A277159 * A277161 A277162 A277163

Keyword

nonn

Author

Eric Rowland, Oct 01 2016

Status

approved