The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 30 15:27 EST 2020. Contains 338807 sequences. (Running on oeis4.)