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A320065 a(n) is the smallest integer i such that binomial(2i,i) > n. 0
1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The formula can be proved by using Stirling's formula to estimate the central binomial coefficient binomial(2i,i).

LINKS

Table of n, a(n) for n=1..103.

FORMULA

a(n) = (log n)/(log 4) + (log log n)/(log 16) + O(1).

MATHEMATICA

Array[Block[{i = 1}, While[Binomial[2 i, i] <= #, i++]; i] &, 105] (* Michael De Vlieger, Oct 22 2018 *)

CROSSREFS

Cf. A000984.

Sequence in context: A069624 A092139 A084558 * A163291 A156875 A066339

Adjacent sequences:  A320062 A320063 A320064 * A320066 A320067 A320068

KEYWORD

nonn

AUTHOR

David Lewis, Oct 22 2018

STATUS

approved

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Last modified September 18 18:15 EDT 2019. Contains 327178 sequences. (Running on oeis4.)