A277157 - OEIS

%I #10 Nov 05 2025 15:22:35

%S 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,

%T 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,

%U 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

%N Lexicographically least sequence of nonnegative integers that avoids 13/7-powers.

%C This sequence is 19-regular.

%C 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.

%H Eric Rowland, <a href="/A277157/b277157.txt">Table of n, a(n) for n = 0..20000</a>

%H Lara Pudwell and Eric Rowland, <a href="https://arxiv.org/abs/1510.02807">Avoiding fractional powers over the natural numbers</a>, arXiv:1510.02807 [math.CO] (2015).

%F a(19 n + 18) = a(n) + 1.

%t (* This gives the first 6859 terms. *)

%t SubstitutionSystem[{n_ :> {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, n + 1}}, {0}, {{3}}]

%Y Cf. A277143, A277149, A277156 (sequences in the same family).

%K nonn

%O 0

%A _Eric Rowland_, Oct 01 2016