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

1,1

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

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

Links

Table of n, a(n) for n=1..62.

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    |_ _ _ _ _ _ _ _|
...

Mathematica

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

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.

Sequence in context: A254760 A279289 A175382 * A325797 A128163 A177088

Adjacent sequences: A279241 A279242 A279243 * A279245 A279246 A279247

Keyword

nonn,changed

Author

Omar E. Pol, Dec 08 2016

Status

approved