

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
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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 (nsquare)th(=n^2) position (n^2+n1) 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), 487495.


LINKS

R. Zumkeller, Table of n, a(n) for n = 0..10000


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



