%N The first representative in A014486 for each equivalence class of non-oriented binary tree corresponding to the oriented (plane) binary tree encoded by A014486(n).
%C Any n that occurs in the sequence, occurs for the first time at n (i.e. a(n)=n), thus there are no cases where a(n) > n. A001190(n+1) distinct values occur in each range [A014137(n-1)..A014138(n-1)]. This sequence is similar to A127302 in that it maps all the plane binary trees which belong to the same equivalence class of non-oriented binary trees to one and same integer and likewise, every Catalan bijection whose signature permutation SP satisfies the condition mentioned in A127302, satisfies in a similar way A153835(SP(n)) = A153835(n).
%H A. Karttunen, <a href="/A153835/b153835.txt">Table of n, a(n) for n = 0..2055</a>
%o (MIT Scheme:) (define (*A153835! s) (cond ((pair? s) (*A153835! (car s)) (*A153835! (cdr s)) (if (= 1 (A154103bi (parenthesization->A014486 (car s)) (parenthesization->A014486 (cdr s)))) (*A069770! s)))) s)
%Y A127302(a(n)) = A127302(n) holds for all n. Cf. A154103, A069770.
%A _Antti Karttunen_, Jan 05 2009