A135034 Positive integers n repeated 2n-1 times, with a leading a(0) = 0. Also: ceiling of square root of n.

0, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9

Offset: 0

Author

William A. Tedeschi, Feb 10 2008

Keywords

• easy
• nonn

Examples

			a(1) = ceiling(sqrt(1)) = 1
a(6) = ceiling(sqrt(6)) = 3
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A005408, A003059 (restriction to positive indices), A000194 (round(sqrt(n))), A000196 (floor(sqrt(n))).

Partial sums of A010052.

Programs

Mathematica

Table[Ceiling[Sqrt[n]],{n,0,100}] (* Mohammad K. Azarian, Jun 15 2016 *)
Table[PadRight[{},2n-1,n],{n,0,10}]//Flatten (* Harvey P. Dale, May 15 2022 *)

PARI

A135034(n)=ceil(sqrt(n)) \\ M. F. Hasler, Nov 12 2017

Python

from math import isqrt
def A135034(n): return isqrt(n-1)+1 if n else 0 # Chai Wah Wu, Nov 04 2024

Formula

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

a(n) = A003059(n), for n >= 1. - R. J. Mathar, Jun 18 2008

Extensions

Edited and corrected by M. F. Hasler, Nov 12 2017