cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A048761 Smallest square greater than or equal to n.

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%I A048761 #40 Aug 15 2022 04:30:27
%S A048761 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 A048761 36,36,36,36,36,36,36,36,36,36,36,49,49,49,49,49,49,49,49,49,49,49,49,
%U A048761 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 A048761 Smallest square greater than or equal to n.
%C A048761 From _M. F. Hasler_, Oct 05 2009: (Start)
%C A048761 For each k > 0, the term k^2 is listed 2k - 1 times.
%C A048761 a(n+1) is the least square greater than n. (End)
%D A048761 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 A048761 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 A048761 Reinhard Zumkeller, <a href="/A048761/b048761.txt">Table of n, a(n) for n = 0..10000</a>
%H A048761 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 A048761 Florentin Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/OPNS.pdf">Only Problems, Not Solutions!</a>.
%F A048761 a(n) = (A000196(n) + 1 - A010052(n))^2. - _Reinhard Zumkeller_, Mar 16 2014
%F A048761 a(n) = (ceiling(sqrt(n)))^2. - _Alonso del Arte_, Jun 21 2015
%F A048761 Sum_{n>=1} 1/a(n)^2 = 2*zeta(3) - Pi^4/90. - _Amiram Eldar_, Aug 15 2022
%p A048761 A048761 := proc(n)
%p A048761         ceil(sqrt(n)) ;
%p A048761         %^2 ;
%p A048761 end proc: # _R. J. Mathar_, Sep 26 2011
%t A048761 (Ceiling[Sqrt[Range[0, 99]]])^2 (* _Alonso del Arte_, Jun 21 2015 *)
%o A048761 (PARI) A048761(n)=if(n,(sqrtint(n-1)+1)^2,0) \\ _M. F. Hasler_, Oct 05 2009
%o A048761 (Haskell)
%o A048761 a048761 n = (a000196 n + 1 - a010052 n) ^ 2
%o A048761 a048761_list = 0 : concat (f 1 1) where
%o A048761    f u v = (take v $ repeat u) : f (u + v + 2) (v + 2)
%o A048761 -- _Reinhard Zumkeller_, Mar 16 2014
%o A048761 (Magma) [Ceiling(Sqrt(n))^2: n in [0..80]]; // _Vincenzo Librandi_, Jun 21 2015
%Y A048761 Cf. A000196, A010052, A048760, A165775.
%K A048761 nonn,easy
%O A048761 0,3
%A A048761 Charles T. Le (charlestle(AT)yahoo.com)
%E A048761 Missing a(49) = 49 inserted by _Reinhard Zumkeller_, Mar 16 2014