

A277143


Lexicographically least sequence of nonnegative integers that avoids 5/3powers.


4



0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0
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OFFSET

0,35


COMMENTS

This sequence is 7regular.
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/bpowers is (2 a  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(7 n + 6) = a(n) + 1.


MATHEMATICA

(* This gives the first 2401 terms. *)
SubstitutionSystem[{n_ :> {0, 0, 0, 0, 1, 0, n + 1}}, {0}, {{4}}]


CROSSREFS

Cf. A277149, A277156, A277157 (sequences in the same family).
Sequence in context: A035187 A291147 A278929 * A239434 A033770 A216283
Adjacent sequences: A277140 A277141 A277142 * A277144 A277145 A277146


KEYWORD

nonn


AUTHOR

Eric Rowland, Oct 01 2016


STATUS

approved



