A277143 - OEIS

A277143

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

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 7-regular.

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.

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: A291147 A278929 A363738 * A239434 A033770 A216283

Adjacent sequences: A277140 A277141 A277142 * A277144 A277145 A277146

KEYWORD

nonn

AUTHOR

Eric Rowland, Oct 01 2016

STATUS

approved