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

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, 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, 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

Offset: 0

Author

Antti Karttunen, Mar 17 2003

Keywords

• nonn

Comments

Apart from the initial term 0, each n occurs A000245(n-1) times.

Crossrefs

Cf. A000108, A000245, A072643, A081289, A081290. Used to compute A081291.

Programs

PARI

A081288(n) = my(i=0); while(binomial(2*i, i)/(i+1) <= n, i++); i; \\ Michel Marcus, Apr 28 2020

Python

from sympy import catalan
def a(n):
    if n==0: return 0
    i=1
    while True:
        if catalan(i)>n: return i
        else: i+=1
print([a(n) for n in range(101)]) # Indranil Ghosh, Jun 08 2017