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%I #11 Nov 08 2016 20:10:33
%S 0,0,0,1,1,1,0,2,0,2,0,1,1,1,0,0,0,2,1,2,0,2,1,1,0,0,0,1,1,2,0,2,0,2,
%T 0,1,0,1,0,1,0,2,0,2,1,1,1,0,0,0,1,2,1,2,0,2,0,1,0,1,0,1,0,2,0,2,0,2,
%U 1,1,0,0,0,1,1,2,0,2,1,1,0,0,0,1,1,2,0,2,0,2,0,1,0,1,0,1,0,2,0,2,1,1,1,0,0,0,1,2,1,2,0,2,0,1,0,1,0,1,0,2
%N Lexicographically least sequence of nonnegative integers that avoids 4/3-powers.
%C This sequence is 56-regular.
%H Eric Rowland, <a href="/A277142/b277142.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(56 n + 73) = 1 if a(n) = 0.
%F a(56 n + 73) = a(n) + 2 if a(n) != 0.
%t (* This gives the first 4162 terms. *)
%t With[{u = {1, 2, 0, 2, 1, 1, 0, 0, 0, 1, 1, 2, 0, 2, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0, 2, 1, 1, 1, 0, 0, 0, 1, 2, 1, 2, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 1, 1, 0, 0, 0}, v = {zero, 0, 0, 1, 1, 1, 0, 2, 0, 2, 0, 1, 1, 1, 0, 0, 0, 2}}, Replace[SubstitutionSystem[{zero -> Join[v, Append[u, 1]], 0 -> Append[u, 1], n_Integer :> Append[u, n + 2]}, {zero}, {{2}}], zero -> 0, {1}]]
%Y Cf. A277141 (the lexicographically least sequence that avoids a/b-powers for all a/b >= 4/3).
%K nonn
%O 0,8
%A _Eric Rowland_, Oct 01 2016
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