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A279244
Numbers k with the property that both the smallest and the largest Dyck path of the symmetric representation of sigma(k) share some line segments.
3
5, 7, 9, 11, 13, 14, 15, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 62, 63, 65, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 79, 81, 82, 83, 85, 86, 87, 89, 91, 92
OFFSET
1,1
COMMENTS
Numbers k such that the symmetric representation of sigma(k) is formed by more than two parts, or that it is formed by only two parts and they do not meet at the center.
Numbers k whose total length of all line segments of the symmetric representation of sigma(k) is < 4*k (cf. A348705). - Omar E. Pol, Nov 02 2021
EXAMPLE
5, 7, 9, 11, 13, 14, and 15 are in the sequence because the smallest and the largest Dyck path of their symmetric representation of sigma share some line segments, as shown below.
Illustration of initial terms:
n
. _ _ _ _ _ _ _
. | | | | | | | | | | | |
. | | | | | | | | | | | |
. _|_| | | | | | | | | | |
. _ _ _| _|_| | | | | | | | |
5 |_ _ _| _| _ _|_| | | | | | |
. _ _ _ _| _| | _ _|_| | | | |
7 |_ _ _ _| |_ _|_| _ _|_| | |
. _ _ _ _ _| _| | _ _ _|_|
9 |_ _ _ _ _| | _|_| |
. _ _ _ _ _ _| _ _| _|
11 |_ _ _ _ _ _| | _| _|
. _ _ _ _ _ _ _| |_ _|
13 |_ _ _ _ _ _ _| |
14 |_ _ _ _ _ _ _ _|
15 |_ _ _ _ _ _ _ _|
...
CROSSREFS
Complement of A279029.
Indices of positive terms in A279228.
Subsequence of A238524.
Sequence in context: A254760 A279289 A175382 * A325797 A128163 A177088
KEYWORD
nonn
AUTHOR
Omar E. Pol, Dec 08 2016
STATUS
approved