login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A337546 A binary sequence defined as follows: a(1)=0; thereafter choose a(n) so as to minimize the number of final consecutive repeated words, and if there is a choice, minimize the length of the repeated word. 3
0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

Start with a(1)=0, then select a(n)=0 or a(n)=1 so as to minimize the largest integer T such that a(0),...,a(n) has a word repeated T times at the end, and if 0 and 1 produce the same T, so as to minimize the length of the longest word repeated T times at the end.

Cousin of the so-called Linus sequence (A006345), which avoids the longest repeated suffix. Conjectures: 1. This is cubefree (the Linus sequence is not cubefree); 2. density of 0's exists and equals 1/2; 3. recurrent and mirror invariant.

This has some similarities with Gijswijt's sequence A090822. - N. J. A. Sloane, Dec 21 2020

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Alessandro Della Corte, Octave program

MathOverflow, The easily bored sequence

Rémy Sigrist, C program for A337546

EXAMPLE

Consider the first case where the sequence differs from the Linus sequence, that is at n=20. Up to n=19 we have: 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0. Then inserting 0 produces a triple at the end, while inserting 1 produces two occurrences of the word 001 at the end and no cubes. Since the number of repetitions counts more than length of the repeated suffix, a(20)=1.

PROG

(C) See Links section.

CROSSREFS

Cf. A006345, A090822.

Sequence in context: A080846 A082401 A157238 * A059448 A283318 A288633

Adjacent sequences:  A337543 A337544 A337545 * A337547 A337548 A337549

KEYWORD

nonn

AUTHOR

Alessandro Della Corte, Nov 22 2020

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 17 08:34 EDT 2021. Contains 343064 sequences. (Running on oeis4.)