A269518 Lexicographically least sequence of nonnegative integers that avoids 3/2-powers.

0, 0, 1, 1, 0, 2, 1, 0, 0, 1, 1, 2, 0, 0, 1, 1, 0, 3, 1, 0, 0, 1, 1, 3, 0, 0, 1, 1, 0, 2, 1, 0, 0, 1, 1, 4, 0, 0, 1, 1, 0, 3, 1, 0, 0, 1, 1, 2, 0, 0, 1, 1, 0, 2, 1, 0, 0, 1, 1, 3, 0, 0, 1, 1, 0, 3, 1, 0, 0, 1, 1, 4, 0, 0, 1, 1, 0, 2, 1, 0, 0, 1, 1, 2, 0, 0, 1, 1, 0, 3, 1, 0, 0, 1, 1, 3, 0, 0, 1, 1, 0, 2, 1, 0, 0, 1, 1, 5, 0, 0, 1, 1, 0, 3, 1, 0, 0, 1, 1, 2

Offset

0,6

Comments

Rowland and Shallit showed that this sequence is 6-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). Also Electronic Journal of Combinatorics, Volume 25(2) (2018), #P2.27

Eric Rowland and Jeffrey Shallit, Avoiding 3/2-powers over the natural numbers, arXiv:1101.3535 [math.CO] (2011).

Eric Rowland and Jeffrey Shallit, Avoiding 3/2-powers over the natural numbers, Discrete Mathematics 312 (2012) 1282-1288.

Formula

a(6 n + 5) = a(n) + 2. - Eric Rowland, Oct 01 2016

Mathematica

(* This gives the first 7776 terms. *)
Replace[SubstitutionSystem[{n_Integer :> {one, 0, zero, 1, one, n + 2}, zero -> {zero, 0, one, 1, zero, 2}, one -> {zero, 0, one, 1, zero, 3}}, {zero}, {{5}}], {zero -> 0, one -> 1}, {1}] (* Eric Rowland, Oct 01 2016 *)

Crossrefs

Cf. A269517 (the lexicographically least sequence that avoids a/b-powers for all a/b >= 3/2).

Sequence in context: A143379 A254605 A335664 * A219840 A343220 A264893

Adjacent sequences: A269515 A269516 A269517 * A269519 A269520 A269521

Keyword

nonn

Author

Eric Rowland, Feb 28 2016

Status

approved