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 A244160 a(0)=0, and for n >= 1, a(n) = the largest k such that k-th Catalan number <= n. 11
 0, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 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, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Apart from 0, each n occurs A000245(n) times. For n >= 1, a(n) gives the largest k such that C(k) <= n, where C(k) stands for the k-th Catalan number, A000108(k). LINKS Michael De Vlieger, Table of n, a(n) for n = 0..4861 FORMULA a(0) = 0, and for n>=1, a(n) = A081288(n)-1. For all n>=1, A000108(a(n)) = A081290(n). EXAMPLE For n=1, the largest k such that C(k) <= 1 is 1, thus a(1) = 1. For n=2, the largest k such that C(k) <= 2 is 2, thus a(2) = 2. For n=3, the largest k such that C(k) <= 3 is 2, thus a(3) = 2. For n=4, the largest k such that C(k) <= 4 is 2, thus a(4) = 2. For n=5, the largest k such that C(k) <= 5 is 3, thus a(5) = 3. MATHEMATICA MapIndexed[ConstantArray[First@ #2 - 1, #1] &, Differences@ Array[CatalanNumber, 8, 0]] /. {} -> {0} // Flatten (* Michael De Vlieger, Jun 08 2017 *) PROG (Scheme) (define (A244160 n) (if (zero? n) n (- (A081288 n) 1))) (Python) from sympy import catalan def a(n):     if n==0: return 0     i=1     while True:         if catalan(i)>n: break         else: i+=1     return i - 1 print [a(n) for n in range(0, 101)] # Indranil Ghosh, Jun 08 2017 CROSSREFS After zero, one less than A081288. Cf. A000108, A000245, A081290, A014418, A239903, A244215, A244159, A236859, A126307. Sequence in context: A086673 A101787 A269024 * A064099 A134021 A330558 Adjacent sequences:  A244157 A244158 A244159 * A244161 A244162 A244163 KEYWORD nonn AUTHOR Antti Karttunen, Jun 23 2014 STATUS approved

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Last modified April 3 23:48 EDT 2020. Contains 333207 sequences. (Running on oeis4.)