

A055228


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


13



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
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OFFSET

0,3


COMMENTS

Axenovich's improvement to the Erdős strong Deltasystem conjecture. Erdős and Rado called a family of sets {A1, A2, .., Ak} a strong Deltasystem 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 nsets {A1, A2, .., Am} contains k sets forming a strong Deltasystem. 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 Liyao 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. FonDerFlaass and A. Kostochka, On set systems without weak 3Deltasubsystems, Discrete Math. 138(1995), 5762.
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), 8590.
P. Erdős and R. Rado, Intersection theorems for systems of finite sets II, J. London Math. Soc. (2) 44(1969), 467479.


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


CROSSREFS

Cf. A000142, A003059.
Sequence in context: A006888 A009589 A098179 * A098642 A079447 A171832
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



