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
Alessandro Della Corte, The Easily Bored Sequence, Univ. of Camerino (2022).
Alessandro Della Corte, The Easily Bored Sequence, Topology and Its Applications 320 (2022), 108244.
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
KEYWORD
nonn
AUTHOR
Alessandro Della Corte, Nov 22 2020
STATUS
approved