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A002984
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a(0) = 1; for n>0, a(n) = a(n-1) + [ sqrt a(n-1) ].
(Formerly M0554)
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9
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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; internal format)
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OFFSET
| 0,2
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COMMENTS
| For n>3 we have a(n) < n^2/4 and for n>44 we have a(n) > n^2/5. - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 17 2006
This sequence contains an infinity of squares . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Apr 03 2009]
This is to floor as A033638 is to round. [Jonathan Vos Post, Oct 08 2011].
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
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FORMULA
| a(n+1) = a(n) + A000196(a(n)). [Reinhard Zumkeller, Dec 28 2011]
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MATHEMATICA
| NestList[ # + Floor[ Sqrt[ # ] ] &, 1, 50 ]
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PROG
| (Haskell)
a002984 n = a002984_list !! n
a002984_list = iterate (\x -> x + a000196 x) 1
-- Reinhard Zumkeller, Dec 28 2011
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CROSSREFS
| Cf. A000302 (subsequence of squares).
Sequence in context: A089649 A049700 * A109965 A008669 A055104 A062435
Adjacent sequences: A002981 A002982 A002983 * A002985 A002986 A002987
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), Dec 14 2000
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