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A028392 a(n) = n + floor(sqrt(n)). 17
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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) position (5) and compact the sequence;

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

....

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

(End)

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

REFERENCES

Problem B4 in L. F. Klosinski, G. L. Alexanderson and A. P. Hillman, The William Lowell Putnam Mathematical Competition, Amer. Math. Monthly 91 (1984), 487-495.

LINKS

R. Zumkeller, Table of n, a(n) for n = 0..10000 [From Reinhard Zumkeller, Oct 14 2010]

FORMULA

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

EXAMPLE

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 + ...

MATHEMATICA

f[n_]:=n+Floor[Sqrt[n]]; Table[f[n], {n, 0, 5!}] (* Vladimir Joseph Stephan Orlovsky, Mar 29 2010 *)

PROG

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

(Haskell)

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

CROSSREFS

Complement of A028387.

Cf. A000196. - Reinhard Zumkeller, Oct 14 2010

Sequence in context: A263579 A166527 A039223 * A175970 A286689 A278373

Adjacent sequences:  A028389 A028390 A028391 * A028393 A028394 A028395

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified September 24 04:27 EDT 2017. Contains 292403 sequences.