A104103 a(n) = ceiling(sqrt(prime(n))).

2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19

Offset: 1

Author

Giovanni Teofilatto, Mar 04 2005

Keywords

• nonn

Comments

Number of squares (including 0) less than prime(n).

Examples

			a(5)=4 because prime(5)=11 and there are 4 squares <= 11, namely 0, 1, 4 and 9.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Programs

Mathematica

Ceiling[Sqrt[Prime[Range[80]]]] (* Harvey P. Dale, May 09 2020 *)

PARI

A104103(n)=sqrtint(prime(n))+1 /* More than twice as fast as the "trivial" implementation using ceil(sqrt(p)), and avoids errors due to insufficient realprecision (although this is unlikely to be an issue, since prime(n) is limited to precomputed primes < primelimit). */ \\ Charles R Greathouse IV and M. F. Hasler, Aug 23 2012

PARI

apply(n->sqrtint(n)+1,primes(100)) \\ Charles R Greathouse IV, Aug 23 2012

Python

from math import isqrt
from sympy import prime
def A104103(n): return 1+isqrt(prime(n)) # Chai Wah Wu, Jul 28 2022

Formula

a(n) = A000196(A000040(n)) + 1. (Although ceiling(sqrt(n)) = A000196(n-1) + 1 in general, the -1 is not needed here since no prime is a square.) - M. F. Hasler, Aug 23 2012

Extensions

Edited by Zak Seidov, Sep 24 2007

Several terms >= 9 corrected, following an observation by Kevin Ryde, by M. F. Hasler, Aug 23 2012