A307095
Let K_n = prefix of length n of Kolakoski sequence A000002; a(n) is the length of the longest palindromic suffix of K_n.
Original entry on oeis.org
1, 1, 2, 4, 2, 4, 3, 3, 2, 4, 6, 5, 7, 2, 4, 3, 5, 7, 9, 11, 13, 3, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 6, 3, 2, 4, 6, 5, 7, 2, 4, 3, 3, 2, 4, 6, 8, 10, 12, 6, 5, 7, 2, 4, 3, 5, 7, 9, 11, 13, 3, 2, 4, 6, 5, 7, 2, 4, 3, 5, 7, 6, 3, 2, 4, 6, 8, 10, 12, 2, 4
Offset: 1
The first terms, alongside K_n with longest palindromic suffix in parentheses, are:
n a(n) K_n
-- ---- ------------------
1 1 (1)
2 1 1(2)
3 2 1(22)
4 4 (1221)
5 2 122(11)
6 4 12(2112)
7 3 1221(121)
8 3 12211(212)
9 2 1221121(22)
10 4 122112(1221)
11 6 12211(212212)
12 5 1221121(22122)
13 7 122112(1221221)
14 2 122112122122(11)
15 4 12211212212(2112)
16 3 1221121221221(121)
See
A220080 for a similar sequence.
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.
Original entry on oeis.org
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, 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, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 18, 20, 22, 24, 26, 28, 30, 32
Offset: 1
n: .. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ...
T-M: a b b a b a a b b a a b a b b a ... (Thue-Morse)
a(n): 1 1 2 4 3 3 2 4 0 0 6 8 10 12 14 16 ...
Corresponding successive maximal palindromic suffixes P:
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), ...
- Rémy Sigrist, Table of n, a(n) for n = 1..16384
- A. Blondin Massé, S. Brlek, and S. Labbé, Combinatorial properties of f-palindromes in the Thue-Morse sequence, Pure Mathematics and Applications 19.2-3 (2008): 39-52.
- A. Blondin Massé, S. Brlek, and S. Labbé, Palindromic lacunas of the Thue-Morse word, GASCom 08 - Proceedings.
- Rémy Sigrist, Perl program for A308182
A308659
a(1)=1; for n > 1, a(n) is the length of the longest palindromic suffix of (a(1), ..., a(n-1)).
Original entry on oeis.org
1, 1, 2, 1, 3, 1, 3, 3, 2, 1, 1, 2, 4, 1, 1, 2, 1, 3, 1, 3, 3, 2, 1, 1, 2, 4, 1, 1, 2, 1, 3, 1, 3, 3, 2, 1, 1, 2, 4, 1, 1, 2, 1, 3, 1, 3, 3, 2, 1, 1, 2, 4, 1, 1, 2, 1, 3, 1, 3, 3, 2, 1, 1, 2, 4, 1, 1, 2, 1, 3, 1, 3, 3, 2, 1, 1, 2, 4, 1, 1, 2, 1, 3, 1, 3, 3, 2
Offset: 1
1
[1], 1
[1 , 1], 2
1 , 1 ,[2], 1
1 ,[1 , 2 , 1], 3
1 , 1 , 2 , 1 ,[3], 1
1 , 1 , 2 ,[1 , 3 , 1], 3
1 , 1 , 2 , 1 ,[3 , 1 , 3], 3
1 , 1 , 2 , 1 , 3 , 1 ,[3 , 3], 2
1 , 1 , 2 , 1 , 3 , 1 , 3 , 3 ,[2], 1
1 , 1 , 2 , 1 , 3 , 1 , 3 , 3 , 2 ,[1], 1
1 , 1 , 2 , 1 , 3 , 1 , 3 , 3 , 2 ,[1 , 1], 2
1 , 1 , 2 , 1 , 3 , 1 , 3 , 3 ,[2 , 1 , 1 , 2], 4
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,1).
Showing 1-3 of 3 results.
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