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.

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

Author

Omar E. Pol, Dec 08 2016

Keywords

• nonn

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

a(n) is also 1 plus the n-th term of the complement of A323648. - Hartmut F. W. Hoft, Feb 22 2025

Examples

			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.

Cf. A000203, A008586, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A279029, A279244, A323648, A348705.

Programs

Mathematica

(* Function a279029Q is defined in A279029 *)
a279244[n_] := Select[Range[n], !a279029Q[#]&]
a279244[92] (* Hartmut F. W. Hoft, Feb 20 2025 *)