OFFSET
1,1
COMMENTS
So far, all the values in the list except the first two are odd numbers.
LINKS
Kevin Ryde, Table of n, a(n) for n = 1..8192
Kevin Ryde, PARI/GP Code
EXAMPLE
For n=3, the length of the longest word in the Period-doubling sequence that admits only unique length-3 factors is a(3) = 7 (attained by word 1000101 and its reversal).
PROG
(Walnut)
def pdfactoreq "At (t<n) => PD[i+t]=PD[j+t]"; % Check if two length-n factors of Period-doubling sequence at positions i and j are equal; PD is predefined in Walnut as the DFA that recognises the Period-doubling sequence. %
def PD_w_len_N_unique_factors "Ei (Aj, k (i<=j & j<(i+n-N) & j<k & k<(i+n-N+1)) => ~$pdfactoreq(j, k, N))": % Find lengths of words with length-N unique factors; must replace N with a constant %
def longest_len_N "$PD_w_len_N_unique_factors(n) & Am (m>n) => ~$PD_w_len_N_unique_factors(m)"; % Check the longest of the lengths found in previous line; must replace N with the same constant %
(PARI) See links.
CROSSREFS
KEYWORD
nonn
AUTHOR
Gandhar Joshi, Oct 24 2023
STATUS
approved