A145445 a(n) = the smallest square > n-th prime.

4, 4, 9, 9, 16, 16, 25, 25, 25, 36, 36, 49, 49, 49, 49, 64, 64, 64, 81, 81, 81, 81, 100, 100, 100, 121, 121, 121, 121, 121, 144, 144, 144, 144, 169, 169, 169, 169, 169, 196, 196, 196, 196, 196, 225, 225, 225, 225, 256, 256, 256, 256, 256, 256, 289, 289, 289, 289

Offset: 1

Author

Zak Seidov, Oct 10 2008

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A104103.

Cf. A000040, A000290, A014085 (run lengths), A245508.

Programs

Haskell

a145445 n = a145445_list !! (n-1)
a145445_list = f a000040_list $ drop 2 a000290_list where
   f ps'@ (p:ps) xs'@(x:xs) = if p < x then x : f ps xs' else f ps' xs
-- Reinhard Zumkeller, Jul 25 2014

Mathematica

Table[Ceiling[Prime[n]^(1/2)]^2,{n,100}]

Python

from sympy import prime, integer_nthroot
def a(n): return (integer_nthroot(prime(n), 2)[0]+1)**2
print([a(n) for n in range(1, 59)]) # Michael S. Branicky, Apr 04 2021

Formula

a(n) = A104103(n)^2.