A081290 a(0) = 0, and for n >=1, a(n) = the largest Catalan number <= n.

0, 1, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42

Offset: 0

Author

Antti Karttunen, Mar 17 2003

Keywords

• nonn

Comments

After n>0, A000108(n) occurs A000245(n) times.

For all n>0, a(A000108(n)) = A000108(n) [the first occurrence of the n-th Catalan number in this sequence].

Minimal i such that A081289(i) >= A081289(n) [the original definition of the sequence].

In other words, the first position k in A081289 where A081289(n) occurs (the minimal k such that A081289(k) = A081289(n)), and also the first position k in A081288 where A081288(n) occurs (the minimal k such that A081288(k) = A081288(n)). The starting point of the run which contains the n-th term in those sequences.

Crossrefs

Cf. A000108, A081288, A081289, A072643, A239903.

Programs

Mathematica

Join[{0},With[{catnos=Reverse[CatalanNumber[Range[10]]]},Table[ SelectFirst[ catnos,#<=n&],{n,80}]]] (* This program uses the SelectFirst function from Mathematica version 10 *) (* Harvey P. Dale, Jul 27 2014 *)

Formula

a(0) = 0, a(n) = A000108(A081288(n)-1).

Sum_{n>=1} 1/a(n)^2 = 44*Pi/sqrt(3) - 4*Pi^2 - 38. - Amiram Eldar, Aug 18 2022

Extensions

Name changed by Antti Karttunen, Apr 26 2014