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A048761
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Smallest square greater than or equal to n.
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18
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0, 1, 4, 4, 4, 9, 9, 9, 9, 9, 16, 16, 16, 16, 16, 16, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81
(list;
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listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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From M. F. Hasler, Oct 05 2009: (Start)
For each k > 0, the term k^2 is listed 2k - 1 times.
a(n+1) is the least square greater than n. (End)
a(n) = (A000196(n) + 1 - A010052(n))^2. - Reinhard Zumkeller, Mar 16 2014
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REFERENCES
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Krassimir Atanassov, On the 40th and 41st Smarandache Problems, Notes on Number Theory and Discrete Mathematics, Sophia, Bulgaria, Vol. 4 (1998), No. 3, 101-104.
J. Castillo, Other Smarandache Type Functions: Inferior/Superior Smarandache f-part of x, Smarandache Notions Journal, Vol. 10, No. 1-2-3, 1999, 202-204.
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Krassimir Atanassov, On Some of Smarandache's Problems, American Research Press, 1999, 27-32.
Florentin Smarandache, Only Problems, Not Solutions!
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FORMULA
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a(n) = (ceiling(sqrt(n)))^2. - Alonso del Arte, Jun 21 2015
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MAPLE
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A048761 := proc(n)
ceil(sqrt(n)) ;
%^2 ;
end proc: # R. J. Mathar, Sep 26 2011
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MATHEMATICA
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(Ceiling[Sqrt[Range[0, 99]]])^2 (* Alonso del Arte, Jun 21 2015 *)
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PROG
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(PARI) A048761(n)=if(n, (sqrtint(n-1)+1)^2, 0) \\ M. F. Hasler, Oct 05 2009
(Haskell)
a048761 n = (a000196 n + 1 - a010052 n) ^ 2
a048761_list = 0 : concat (f 1 1) where
f u v = (take v $ repeat u) : f (u + v + 2) (v + 2)
-- Reinhard Zumkeller, Mar 16 2014
(MAGMA) [Ceiling(Sqrt(n))^2: n in [0..80]]; // Vincenzo Librandi, Jun 21 2015
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CROSSREFS
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Cf. A165775.
Sequence in context: A065734 A288797 A200600 * A211547 A075561 A256796
Adjacent sequences: A048758 A048759 A048760 * A048762 A048763 A048764
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KEYWORD
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nonn,easy
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AUTHOR
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Charles T. Le (charlestle(AT)yahoo.com)
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EXTENSIONS
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Missing a(49) = 49 inserted by Reinhard Zumkeller, Mar 16 2014
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STATUS
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approved
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