A048761 Smallest square greater than or equal to n.

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

Offset

0,3

Comments

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)

References

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.

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.

Links

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!.

Formula

a(n) = (A000196(n) + 1 - A010052(n))^2. - Reinhard Zumkeller, Mar 16 2014

a(n) = (ceiling(sqrt(n)))^2. - Alonso del Arte, Jun 21 2015

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

Maple

A048761 := proc(n)
        ceil(sqrt(n)) ;
        %^2 ;
end proc: # R. J. Mathar, Sep 26 2011

Mathematica

(Ceiling[Sqrt[Range[0, 99]]])^2 (* Alonso del Arte, Jun 21 2015 *)

Prog

(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

Crossrefs

Cf. A000196, A010052, A048760, A165775.

Sequence in context: A065734 A288797 A200600 * A211547 A075561 A376073

Adjacent sequences: A048758 A048759 A048760 * A048762 A048763 A048764

Keyword

nonn,easy

Author

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

Extensions

Missing a(49) = 49 inserted by Reinhard Zumkeller, Mar 16 2014

Status

approved