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 A002984 a(0) = 1; for n > 0, a(n) = a(n-1) + floor(sqrt(a(n-1))). (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 (list; graph; refs; listen; history; text; internal format)
 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. Adams-Watters, 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 EXTENSIONS More terms from Larry Reeves (larryr(AT)acm.org), Dec 14 2000 STATUS approved

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Last modified April 18 22:45 EDT 2021. Contains 343098 sequences. (Running on oeis4.)