A221205 a(n) is the nearest integer to sqrt(pi(10^n)) (see A006880).

0, 2, 5, 13, 35, 98, 280, 815, 2400, 7131, 21332, 64172, 193928, 588273, 1790235, 5463018, 16710426, 51220671, 157289397, 483795067, 1490241458, 4596440959, 14193917243, 43878472986, 135777758736, 420530985064, 1303551591182, 4043817556078, 12553456467283, 38996129419652

Offset: 0

Author

Vladimir Pletser, Jan 04 2013

Keywords

• nonn

Comments

Nearest integer to sqrt(pi(10^n)) where pi(10^n) is the number of primes < 10^n (A006880).

Crossrefs

Cf. A006880.

Programs

Mathematica

Array[Round@ Sqrt@ PrimePi[10^#] &, 17, 0] (* Michael De Vlieger, Mar 19 2021 *)

PARI

a(n) = round(sqrt(primepi(10^n))); \\ Michel Marcus, Mar 19 2021

Python

from math import isqrt
from sympy import primepi
def A221205(n): return (m:=isqrt(k:=int(primepi(10**n))))+int(k-m*(m+1)>=1) # Chai Wah Wu, Jul 31 2022

Formula

a(n) = round(sqrt(A006880(n))).

Extensions

a(21) to a(24) added by Vladimir Pletser, Feb 27 2013 (recovered by Georg Fischer, Jan 20 2019)

a(25)-a(28), obtained using A006880, added by Eduard Roure Perdices, Apr 16 2021

a(29), obtained using A006880, added by Chai Wah Wu, Jul 31 2022