cp's OEIS Frontend

A308182 Let S_n = prefix of length n of Thue-Morse sequence A010060; let P = longest palindromic suffix of S_n; a(n) = length of P if P occurs just once as a factor of S_n, otherwise a(n) = 0.

%I A308182 #25 Jun 05 2019 00:40:01
%S A308182 1,1,2,4,3,3,2,4,0,0,6,8,10,12,14,16,6,8,10,12,6,8,10,12,0,0,6,8,10,
%T A308182 12,14,16,0,0,0,0,0,0,0,0,18,20,22,24,26,28,30,32,34,36,38,40,42,44,
%U A308182 46,48,50,52,54,56,58,60,62,64,18,20,22,24,26,28,30,32
%N A308182 Let S_n = prefix of length n of Thue-Morse sequence A010060; let P = longest palindromic suffix of S_n; a(n) = length of P if P occurs just once as a factor of S_n, otherwise a(n) = 0.
%C A308182 The positions of the 0's are the lacunae.
%H A308182 Rémy Sigrist, <a href="/A308182/b308182.txt">Table of n, a(n) for n = 1..16384</a>
%H A308182 A. Blondin Massé, S. Brlek, and S. Labbé, <a href="http://puma.dimai.unifi.it/19_2_3/4.pdf">Combinatorial properties of f-palindromes in the Thue-Morse sequence</a>, Pure Mathematics and Applications 19.2-3 (2008): 39-52.
%H A308182 A. Blondin Massé, S. Brlek, and S. Labbé, <a href="http://www.lacim.uqam.ca/~brlek/Recherche/ListePublis/Articles/GASCom08.pdf">Palindromic lacunas of the Thue-Morse word</a>, GASCom 08 - Proceedings.
%H A308182 Rémy Sigrist, <a href="/A308182/a308182.pl.txt">Perl program for A308182</a>
%F A308182 a(n) equals A220080(n) or 0. - _Rémy Sigrist_, Jun 04 2019
%e A308182 n: .. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ...
%e A308182 T-M:  a b b a b a a b b  a  a  b  a  b  b  a ... (Thue-Morse)
%e A308182 a(n): 1 1 2 4 3 3 2 4 0  0  6  8 10 12 14 16 ...
%e A308182 Corresponding successive maximal palindromic suffixes P:
%e A308182 a (so a(1)=1), b, bb, abba (so a(4)=4), bab, aba, aa, baab, bb (but bb has already appeared, so a(9)=0), ...
%o A308182 (Perl) See Links section.
%Y A308182 Cf. A010060, A220080.
%K A308182 nonn
%O A308182 1,3
%A A308182 _N. J. A. Sloane_, Jun 04 2019
%E A308182 More terms from _Rémy Sigrist_, Jun 04 2019