A343621 Numbers k such that the largest Dyck path of the symmetric representation of sigma(k) does not touch the largest Dyck path of the symmetric representation of sigma(k+1).

1, 3, 5, 7, 11, 15, 17, 19, 23, 27, 29, 31, 35, 39, 41, 47, 53, 55, 59, 63, 65, 71, 79, 83, 87, 89, 95, 99, 103, 107, 111, 119, 125, 127, 131, 139, 143, 149, 155, 159, 161, 167, 175, 179, 191, 195, 197, 199, 203, 207, 209, 215, 219, 223, 227, 233, 239, 251, 255

Offset: 1

Author

Omar E. Pol, Aug 04 2021

Keywords

• nonn

Comments

This property of a(n) is because the symmetric representation of sigma(a(n)+1) has only one part.

All terms are odd.

First differs from A085493 at a(22).

Links

• Hartmut F. W. Hoft, Table of n, a(n) for n = 1..1390

Crossrefs

Cf. A000203, A085493, A174973, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A239931, A239932, A239933, A239934, A262626, A343621.

Programs

Mathematica

(* Functions a174973Q[ ] is defined in A279029 *)
a343621[n_] := Select[Range[n], a174973Q[#+1]&]
a343621[255] (* Hartmut F. W. Hoft, Feb 20 2025 *)

Formula

a(n) = A174973(n+1) - 1.