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A081288 a(n) is the minimal i such that A000108(i) > n.

%I A081288 #18 Mar 25 2021 10:22:40
%S A081288 0,2,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
%T A081288 5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
%U A081288 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6
%N A081288 a(n) is the minimal i such that A000108(i) > n.
%C A081288 Apart from the initial term 0, each n occurs A000245(n-1) times.
%o A081288 (Python)
%o A081288 from sympy import catalan
%o A081288 def a(n):
%o A081288     if n==0: return 0
%o A081288     i=1
%o A081288     while True:
%o A081288         if catalan(i)>n: return i
%o A081288         else: i+=1
%o A081288 print([a(n) for n in range(101)]) # _Indranil Ghosh_, Jun 08 2017
%o A081288 (PARI) A081288(n) = my(i=0); while(binomial(2*i, i)/(i+1) <= n, i++); i; \\ _Michel Marcus_, Apr 28 2020
%Y A081288 Cf. A000108, A000245, A072643, A081289, A081290. Used to compute A081291.
%K A081288 nonn
%O A081288 0,2
%A A081288 _Antti Karttunen_, Mar 17 2003