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

1,1

Comments

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

Links

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

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Sequence in context: A320297 A165906 A165907 * A194964 A029923 A096029

Adjacent sequences: A104100 A104101 A104102 * A104104 A104105 A104106

Keyword

nonn

Author

Giovanni Teofilatto, Mar 04 2005

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

Status

approved