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 A002984 a(0) = 1; for n>0, a(n) = a(n-1) + floor( sqrt a(n-1) ). (Formerly M0554) 9

%I M0554

%S 1,2,3,4,6,8,10,13,16,20,24,28,33,38,44,50,57,64,72,80,88,97,106,116,

%T 126,137,148,160,172,185,198,212,226,241,256,272,288,304,321,338,356,

%U 374,393,412,432,452,473,494,516,538,561,584,608,632,657,682,708,734

%N a(0) = 1; for n>0, a(n) = a(n-1) + floor( sqrt a(n-1) ).

%C For n>3 we have a(n) < n^2/4 and for n>44 we have a(n) > n^2/5. - _Stefan Steinerberger_, Apr 17 2006

%C This sequence contains an infinity of squares . [_Philippe DELEHAM_, Apr 03 2009]

%C This is to floor as A033638 is to round. [_Jonathan Vos Post_, Oct 08 2011].

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

%H T. D. Noe, <a href="/A002984/b002984.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n+1) = a(n) + A000196(a(n)). [_Reinhard Zumkeller_, Dec 28 2011]

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

%o a002984 n = a002984_list !! n

%o a002984_list = iterate (\x -> x + a000196 x) 1

%o -- _Reinhard Zumkeller_, Dec 28 2011

%o (MAGMA) [n le 0 select 1 else Self(n)+Floor(Sqrt(Self(n))): n in [0..60]]; // _Bruno Berselli_, Feb 15 2013

%Y Cf. A000302 (subsequence of squares).

%Y Essentially the same as A109965.

%K nonn,easy,nice

%O 0,2

%A _N. J. A. Sloane_.

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

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