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Smallest square greater than or equal to n.
20

%I #40 Aug 15 2022 04:30:27

%S 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,

%T 36,36,36,36,36,36,36,36,36,36,36,49,49,49,49,49,49,49,49,49,49,49,49,

%U 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

%N Smallest square greater than or equal to n.

%C From _M. F. Hasler_, Oct 05 2009: (Start)

%C For each k > 0, the term k^2 is listed 2k - 1 times.

%C a(n+1) is the least square greater than n. (End)

%D Krassimir Atanassov, On the 40th and 41st Smarandache Problems, Notes on Number Theory and Discrete Mathematics, Sophia, Bulgaria, Vol. 4, No. 3 (1998), 101-104.

%D 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.

%H Reinhard Zumkeller, <a href="/A048761/b048761.txt">Table of n, a(n) for n = 0..10000</a>

%H Krassimir Atanassov, <a href="http://www.gallup.unm.edu/~smarandache/Atanassov-SomeProblems.pdf">On Some of Smarandache's Problems</a>, American Research Press, 1999, 27-32.

%H Florentin Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/OPNS.pdf">Only Problems, Not Solutions!</a>.

%F a(n) = (A000196(n) + 1 - A010052(n))^2. - _Reinhard Zumkeller_, Mar 16 2014

%F a(n) = (ceiling(sqrt(n)))^2. - _Alonso del Arte_, Jun 21 2015

%F Sum_{n>=1} 1/a(n)^2 = 2*zeta(3) - Pi^4/90. - _Amiram Eldar_, Aug 15 2022

%p A048761 := proc(n)

%p ceil(sqrt(n)) ;

%p %^2 ;

%p end proc: # _R. J. Mathar_, Sep 26 2011

%t (Ceiling[Sqrt[Range[0, 99]]])^2 (* _Alonso del Arte_, Jun 21 2015 *)

%o (PARI) A048761(n)=if(n,(sqrtint(n-1)+1)^2,0) \\ _M. F. Hasler_, Oct 05 2009

%o (Haskell)

%o a048761 n = (a000196 n + 1 - a010052 n) ^ 2

%o a048761_list = 0 : concat (f 1 1) where

%o f u v = (take v $ repeat u) : f (u + v + 2) (v + 2)

%o -- _Reinhard Zumkeller_, Mar 16 2014

%o (Magma) [Ceiling(Sqrt(n))^2: n in [0..80]]; // _Vincenzo Librandi_, Jun 21 2015

%Y Cf. A000196, A010052, A048760, A165775.

%K nonn,easy

%O 0,3

%A Charles T. Le (charlestle(AT)yahoo.com)

%E Missing a(49) = 49 inserted by _Reinhard Zumkeller_, Mar 16 2014