A055228 a(n) = ceiling(sqrt(n!)).

1, 1, 2, 3, 5, 11, 27, 71, 201, 603, 1905, 6318, 21887, 78912, 295260, 1143536, 4574144, 18859678, 80014835, 348776577, 1559776269, 7147792819, 33526120083, 160785623546, 787685471323, 3938427356615, 20082117944246, 104349745809074, 552166953567229

Offset

0,3

Comments

Axenovich's improvement to the Erdős strong Delta-system conjecture. Erdős and Rado called a family of sets {A1, A2, .., Ak} a strong Delta-system if all the intersections Ai INTERSECT Aj are identical, 1 <= i < j <= k. Denoting by f(n,k) the smallest integer m for which every family of n-sets {A1, A2, .., Am} contains k sets forming a strong Delta-system. Then Axenovich et al. proved f(n,3) < (n!)^((1/2) + epsilon)) < a(n) holds for every epsilon > 0, provided n is sufficiently large. - Jonathan Vos Post, Apr 29 2007; typos fixed by Li-yao Xia, May 06 2014

For n>0, a(n) is the least m>0 such that n! <= m^2. - Clark Kimberling, Jul 18 2012

Links

Chai Wah Wu, Table of n, a(n) for n = 0..807 (n = 0..300 from T. D. Noe)

M. Axenovich, D. Fon-Der-Flaass and A. Kostochka, On set systems without weak 3-Delta-subsystems, Discrete Math. 138(1995), 57-62.

Bela Bollobas, To Prove and Conjecture: Paul Erdős and His Mathematics, Am. Math. Monthly, 105 (March 1998)3, p. 232.

P. Erdős and R. Rado, Intersection theorems for systems of finite sets I, J. London Math. Soc. (2) 35(1960), 85-90.

P. Erdős and R. Rado, Intersection theorems for systems of finite sets II, J. London Math. Soc. (2) 44(1969), 467-479.

Formula

a(n) = A003059(A000142(n)). - Jonathan Vos Post, Apr 29 2007

Maple

A055228:=n->ceil(sqrt(n!)); seq(A055228(n), n=0..30); # Wesley Ivan Hurt, May 06 2014

Mathematica

Table[Ceiling[Sqrt[n!]], {n, 0, 30}] (* Wesley Ivan Hurt, May 06 2014 *)

Prog

(PARI) a(n) = ceil(sqrt(n!)) \\ Michel Marcus, Jul 30 2013
(Python)
from math import isqrt, factorial
def A055228(n): return 1+isqrt(factorial(n)-1) # Chai Wah Wu, Jul 28 2022

Crossrefs

Cf. A000142, A003059.

Sequence in context: A006888 A009589 A098179 * A173758 A098642 A079447

Adjacent sequences: A055225 A055226 A055227 * A055229 A055230 A055231

Keyword

easy,nonn

Author

Henry Bottomley, Jun 21 2000

Extensions

A comment stating that one of the terms was wrong has been deleted - the terms are correct. - T. D. Noe, Apr 22 2009

More terms from Wesley Ivan Hurt, May 06 2014

Status

approved