A028392 a(n) = n + floor(sqrt(n)).

0, 2, 3, 4, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 79

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

A171746 gives number of iterations to reach a square. - Reinhard Zumkeller, Oct 14 2010

From Carmine Suriano, Oct 15 2010: (Start)

Also the sequence of integers left after performing the following procedure:

1. Remove the element at 1st position (1) and compact the sequence;

2. Remove the element at 4th (2^2-th) position (5) and compact the sequence;

3. Remove the element at 9th (3^2-th) position (11) and compact the sequence;

....

n. Remove the element at (n-square)th position (n^2 + n - 1) and compact the sequence;

(End)

Examples

			G.f. = 2*x + 3*x^2 + 4*x^3 + 6*x^4 + 7*x^5 + 8*x^6 + 9*x^7 + 10*x^8 + 12*x^9 + ...
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• L. F. Klosinski, G. L. Alexanderson and A. P. Hillman, The William Lowell Putnam Mathematical Competition: Problem B4, Amer. Math. Monthly 91 (1984), 487-495.

Crossrefs

Complement of A028387.

Cf. A000196. - Reinhard Zumkeller, Oct 14 2010

Programs

Haskell

a028392 n = n + a000196 n  -- Reinhard Zumkeller, Oct 28 2012

Mathematica

Table[n + Floor[Sqrt[n]], {n, 0, 99}] (* Vladimir Joseph Stephan Orlovsky, Mar 29 2010 *)

PARI

{a(n) = if( n<0, 0, n + sqrtint(n))}; /* Michael Somos, Jun 11 2003 */

Python

from math import isqrt
def A028392(n): return n+isqrt(n) # Chai Wah Wu, May 16 2023

Scala

(0 to 99).map(n => (n + Math.floor(Math.sqrt(n))).toInt) // Alonso del Arte, Nov 03 2019

Formula

a(n) = 2*n - A028391(n).

G.f.: x / (1 - x)^2 + (theta3(x) - 1) / (2 * (1 - x)). - Michael Somos, Mar 24 2012