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%I #11 Nov 08 2016 20:25:13
%S 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,
%T 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,
%U 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
%N Lexicographically least sequence of nonnegative integers that avoids 13/8-powers.
%C This sequence is 33-regular.
%C 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.
%H Eric Rowland, <a href="/A277160/b277160.txt">Table of n, a(n) for n = 0..20000</a>
%H Lara Pudwell and Eric Rowland, <a href="http://arxiv.org/abs/1510.02807">Avoiding fractional powers over the natural numbers</a>, arXiv:1510.02807 [math.CO] (2015).
%F a(33 n + 32) = a(n) + 1.
%t (* This gives the first 35937 terms. *)
%t 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}}]
%Y Cf. A277155 (sequence in the same family).
%K nonn
%O 0
%A _Eric Rowland_, Oct 01 2016
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