This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A081290 #27 Aug 18 2022 10:31:49
%S A081290 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,
%T A081290 14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,42,42,42,42,42,42,42,42,
%U A081290 42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42
%N A081290 a(0) = 0, and for n >=1, a(n) = the largest Catalan number <= n.
%C A081290 After n>0, A000108(n) occurs A000245(n) times.
%C A081290 For all n>0, a(A000108(n)) = A000108(n) [the first occurrence of the n-th Catalan number in this sequence].
%C A081290 Minimal i such that A081289(i) >= A081289(n) [the original definition of the sequence].
%C A081290 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.
%F A081290 a(0) = 0, a(n) = A000108(A081288(n)-1).
%F A081290 Sum_{n>=1} 1/a(n)^2 = 44*Pi/sqrt(3) - 4*Pi^2 - 38. - _Amiram Eldar_, Aug 18 2022
%t A081290 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 *)
%Y A081290 Cf. A000108, A081288, A081289, A072643, A239903.
%K A081290 nonn
%O A081290 0,3
%A A081290 _Antti Karttunen_, Mar 17 2003
%E A081290 Name changed by _Antti Karttunen_, Apr 26 2014