A366462 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.

2, 4, 7, 9, 11, 15, 17, 19, 21, 23, 25, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161

Offset: 1

Author

Gandhar Joshi, Oct 24 2023

Keywords

• nonn

Comments

So far, all the values in the list except the first two are odd numbers.

Examples

			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).
		

Links

• Kevin Ryde, Table of n, a(n) for n = 1..8192
• Kevin Ryde, PARI/GP Code

Crossrefs

Cf. A096268, A275202 (subword complexity).

Programs

PARI

\\ See links.

Walnut

def pdfactoreq "At (t 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 ~$pdfactoreq(j, k, N))": % Find lengths of words with length-N unique factors; must replace N with a constant %
def longest_len_N "$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 %