A230775 Smallest prime number greater than or equal to the square root of n.

2, 2, 2, 2, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11

Offset: 1

Author

Jean-Christophe Hervé, Nov 01 2013

Keywords

• nonn
• easy

Comments

Or repeat prime(k) (prime(k)^2-prime(k-1)^2) times, with prime(0) set to 0 for k=1.

Examples

			a(5)=a(6)=a(7)=a(8)=a(9)=3 because prime(1)= 2 < sqrt(5 to 9) <= prime(2) = 3.
		

Links

• Jean-Christophe Hervé, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A230774, A050216, A056813.

Programs

Mathematica

spn[n_]:=Module[{s=Sqrt[n]},If[PrimeQ[s],s,NextPrime[s]]]; Array[spn,90] (* Harvey P. Dale, Feb 10 2019 *)

Python

from math import isqrt
from sympy import nextprime
def A230775(n): return nextprime(isqrt(n-1)) # Chai Wah Wu, Nov 04 2024

Formula

a(n) = A000040(A230774(n)).

Repeat prime(1) prime(1)^2 times; for k>1, repeat A000040(k) A050216(k-1) times (that is, repeat prime(k) (prime(k)^2 - prime(k-1)^2) times).