

A002984


a(0) = 1; for n > 0, a(n) = a(n1) + floor(sqrt(a(n1))).
(Formerly M0554)


9



1, 2, 3, 4, 6, 8, 10, 13, 16, 20, 24, 28, 33, 38, 44, 50, 57, 64, 72, 80, 88, 97, 106, 116, 126, 137, 148, 160, 172, 185, 198, 212, 226, 241, 256, 272, 288, 304, 321, 338, 356, 374, 393, 412, 432, 452, 473, 494, 516, 538, 561, 584, 608, 632, 657, 682, 708, 734
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OFFSET

0,2


COMMENTS

For n > 3 we have a(n) < n^2/4; for n > 44 we have a(n) > n^2/5.  Stefan Steinerberger, Apr 17 2006
This sequence contains infinitely many squares.  Philippe Deléham, Apr 03 2009
This is to floor as A033638 is to round.  Jonathan Vos Post, Oct 08 2011
The squares in this sequence are precisely the powers of 4.  Franklin T. AdamsWatters, Jan 06 2014


REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000


FORMULA

a(n+1) = a(n) + A000196(a(n)).  Reinhard Zumkeller, Dec 28 2011


MATHEMATICA

NestList[ # + Floor[ Sqrt[ # ] ] &, 1, 50 ]


PROG

(Haskell)
a002984 n = a002984_list !! n
a002984_list = iterate (\x > x + a000196 x) 1
 Reinhard Zumkeller, Dec 28 2011
(MAGMA) [n le 0 select 1 else Self(n)+Floor(Sqrt(Self(n))): n in [0..60]]; // Bruno Berselli, Feb 15 2013


CROSSREFS

Cf. A000302 (subsequence of squares).
Essentially the same as A109965.
Sequence in context: A008748 A089649 A049700 * A109965 A008669 A055104
Adjacent sequences: A002981 A002982 A002983 * A002985 A002986 A002987


KEYWORD

nonn,easy,nice


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Larry Reeves (larryr(AT)acm.org), Dec 14 2000


STATUS

approved



