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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).

%I A343621 #31 Feb 22 2025 14:53:25
%S A343621 1,3,5,7,11,15,17,19,23,27,29,31,35,39,41,47,53,55,59,63,65,71,79,83,
%T A343621 87,89,95,99,103,107,111,119,125,127,131,139,143,149,155,159,161,167,
%U A343621 175,179,191,195,197,199,203,207,209,215,219,223,227,233,239,251,255
%N 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).
%C A343621 This property of a(n) is because the symmetric representation of sigma(a(n)+1) has only one part.
%C A343621 All terms are odd.
%C A343621 First differs from A085493 at a(22).
%H A343621 Hartmut F. W. Hoft, <a href="/A343621/b343621.txt">Table of n, a(n) for n = 1..1390</a>
%F A343621 a(n) = A174973(n+1) - 1.
%t A343621 (* Functions a174973Q[ ] is defined in A279029 *)
%t A343621 a343621[n_] := Select[Range[n], a174973Q[#+1]&]
%t A343621 a343621[255] (* _Hartmut F. W. Hoft_, Feb 20 2025 *)
%Y A343621 Cf. A000203, A085493, A174973, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A239931, A239932, A239933, A239934, A262626, A343621.
%K A343621 nonn
%O A343621 1,2
%A A343621 _Omar E. Pol_, Aug 04 2021