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

0,3

Links

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

Formula

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

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

Example

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

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 *)

Prog

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

Crossrefs

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

Partial sums of A010052.

Sequence in context: A186189 A083375 A088519 * A003059 A325678 A247189

Adjacent sequences: A135031 A135032 A135033 * A135035 A135036 A135037

Keyword

easy,nonn

Author

William A. Tedeschi, Feb 10 2008

Extensions

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

Status

approved