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%I #26 Dec 13 2021 17:26:10
%S 5,7,9,11,13,14,15,17,19,21,22,23,25,26,27,29,31,33,34,35,37,38,39,41,
%T 43,44,45,46,47,49,50,51,52,53,55,57,58,59,61,62,63,65,67,68,69,70,71,
%U 73,74,75,76,77,79,81,82,83,85,86,87,89,91,92
%N 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.
%C 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.
%C 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
%e 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.
%e Illustration of initial terms:
%e n
%e . _ _ _ _ _ _ _
%e . | | | | | | | | | | | |
%e . | | | | | | | | | | | |
%e . _|_| | | | | | | | | | |
%e . _ _ _| _|_| | | | | | | | |
%e 5 |_ _ _| _| _ _|_| | | | | | |
%e . _ _ _ _| _| | _ _|_| | | | |
%e 7 |_ _ _ _| |_ _|_| _ _|_| | |
%e . _ _ _ _ _| _| | _ _ _|_|
%e 9 |_ _ _ _ _| | _|_| |
%e . _ _ _ _ _ _| _ _| _|
%e 11 |_ _ _ _ _ _| | _| _|
%e . _ _ _ _ _ _ _| |_ _|
%e 13 |_ _ _ _ _ _ _| |
%e 14 |_ _ _ _ _ _ _ _|
%e 15 |_ _ _ _ _ _ _ _|
%e ...
%Y Complement of A279029.
%Y Indices of positive terms in A279228.
%Y Subsequence of A238524.
%Y Cf. A000203, A008586, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A348705.
%K nonn
%O 1,1
%A _Omar E. Pol_, Dec 08 2016
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