|
%I #27 Nov 02 2023 10:40:37
%S 2,4,7,9,11,15,17,19,21,23,25,31,33,35,37,39,41,43,45,47,49,51,53,63,
%T 65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,97,99,101,103,105,
%U 107,109,127,129,131,133,135,137,139,141,143,145,147,149,151,153,155,157,159,161
%N a(n) is the length of the longest word w in the Period-doubling sequence (A096268) in which every length-n factor of w is unique.
%C So far, all the values in the list except the first two are odd numbers.
%H Kevin Ryde, <a href="/A366462/b366462.txt">Table of n, a(n) for n = 1..8192</a>
%H Kevin Ryde, <a href="/A366462/a366462.gp.txt">PARI/GP Code</a>
%e 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).
%o (Walnut)
%o 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. %
%o def PD_w_len_N_unique_factors "Ei (Aj, k (i<=j & j<(i+n-N) & j<k & k<(i+n-N+1)) => ~$pdfactoreq(j, k, N))": % Find lengths of words with length-N unique factors; must replace N with a constant %
%o def longest_len_N "$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 %
%o (PARI) See links.
%Y Cf. A096268, A275202 (subword complexity).
%K nonn
%O 1,1
%A _Gandhar Joshi_, Oct 24 2023
|
