cp's OEIS Frontend

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.

%I A279244 #45 Mar 05 2025 20:10:22
%S A279244 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 A279244 43,44,45,46,47,49,50,51,52,53,55,57,58,59,61,62,63,65,67,68,69,70,71,
%U A279244 73,74,75,76,77,79,81,82,83,85,86,87,89,91,92
%N 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.
%C A279244 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 A279244 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
%C A279244 a(n) is also 1 plus the n-th term of the complement of A323648. - _Hartmut F. W. Hoft_, Feb 22 2025
%e A279244 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 A279244 Illustration of initial terms:
%e A279244 n
%e A279244 .              _   _   _   _   _ _ _
%e A279244 .             | | | | | | | | | | | |
%e A279244 .             | | | | | | | | | | | |
%e A279244 .            _|_| | | | | | | | | | |
%e A279244 .      _ _ _|    _|_| | | | | | | | |
%e A279244 5     |_ _ _|  _|  _ _|_| | | | | | |
%e A279244 .      _ _ _ _|  _| |  _ _|_| | | | |
%e A279244 7     |_ _ _ _| |_ _|_|    _ _|_| | |
%e A279244 .      _ _ _ _ _|  _|     |  _ _ _|_|
%e A279244 9     |_ _ _ _ _| |      _|_| |
%e A279244 .      _ _ _ _ _ _|  _ _|    _|
%e A279244 11    |_ _ _ _ _ _| |  _|  _|
%e A279244 .      _ _ _ _ _ _ _| |_ _|
%e A279244 13    |_ _ _ _ _ _ _| |
%e A279244 14    |_ _ _ _ _ _ _ _|
%e A279244 15    |_ _ _ _ _ _ _ _|
%e A279244 ...
%t A279244 (* Function a279029Q is defined in A279029 *)
%t A279244 a279244[n_] := Select[Range[n], !a279029Q[#]&]
%t A279244 a279244[92] (* _Hartmut F. W. Hoft_, Feb 20 2025 *)
%Y A279244 Complement of A279029.
%Y A279244 Indices of positive terms in A279228.
%Y A279244 Subsequence of A238524.
%Y A279244 Cf. A000203, A008586, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A279029, A279244, A323648, A348705.
%K A279244 nonn
%O A279244 1,1
%A A279244 _Omar E. Pol_, Dec 08 2016