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

0,2

Comments

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

Links

Table of n, a(n) for n=0..29.

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A006880.

Sequence in context: A086581 A059027 A025198 * A037247 A308273 A126221

Adjacent sequences: A221202 A221203 A221204 * A221206 A221207 A221208

Keyword

nonn

Author

Vladimir Pletser, Jan 04 2013

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

Status

approved