A279029 Numbers k with the property that the smallest and the largest Dyck path of the symmetric representation of sigma(k) do not share line segments.

1, 2, 3, 4, 6, 8, 10, 12, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 48, 54, 56, 60, 64, 66, 72, 78, 80, 84, 88, 90, 96, 100, 104, 108, 112, 120, 126, 128, 132, 136, 140, 144, 150, 156, 160, 162, 168, 176, 180, 192, 196, 198, 200, 204, 208, 210, 216, 220, 224, 228, 234, 240, 252, 256

Offset

1,2

Comments

Numbers k such that the symmetric representation of sigma(k) is formed by only one part, or that it's formed by only two parts and they meet at the center.

Numbers k whose total length of all line segments of the symmetric representation of sigma(k) is equal to 4*k (cf. A348705). For the positive integers k that are not in this sequence the mentioned total length is < 4*k. - Omar E. Pol, Nov 02 2021

Links

Table of n, a(n) for n=1..64.

Example

1, 2, 3, 4, 6, 8, 10, 12 and 16 are in the sequence because the smallest and the largest Dyck path of their symmetric representation of sigma do not share line segments, as shown below.
llustration of initial terms:
n
.      _ _ _ _   _   _   _   _       _
1     |_| | | | | | | | | | | |     | |
2     |_ _|_| | | | | | | | | |     | |
3     |_ _|  _|_| | | | | | | |     | |
4     |_ _ _|    _|_| | | | | |     | |
       _ _ _|  _|  _ _|_| | | |     | |
6     |_ _ _ _|  _| |  _ _|_| |     | |
       _ _ _ _| |_ _|_|    _ _|     | |
8     |_ _ _ _ _|  _|     |    _ _ _| |
       _ _ _ _ _| |      _|   |  _ _ _|
10    |_ _ _ _ _ _|  _ _|    _| |
       _ _ _ _ _ _| |      _|  _|
12    |_ _ _ _ _ _ _|  _ _|  _|
                      |  _ _|
                      | |
       _ _ _ _ _ _ _ _| |
16    |_ _ _ _ _ _ _ _ _|
...

Crossrefs

UNION of A174973 and A262259.

Indices of nonzero terms in A279228.

Complement is A279244.

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

Sequence in context: A359754 A330899 A325796 * A316886 A309943 A002093

Adjacent sequences: A279026 A279027 A279028 * A279030 A279031 A279032

Keyword

nonn

Author

Omar E. Pol, Dec 08 2016

Status

approved