A138813 - OEIS

A138813

a(0) = 1; thereafter, a(n) = Sum_{k=0..n-1} ceiling(n/a(k)).

1, 1, 4, 7, 10, 14, 17, 20, 24, 28, 31, 35, 38, 42, 45, 50, 53, 57, 61, 64, 67, 73, 77, 80, 83, 88, 91, 94, 97, 104, 107, 111, 115, 119, 122, 126, 131, 135, 138, 142, 145, 151, 154, 160, 163, 167, 171, 174, 177, 182, 186, 191, 195, 199, 203, 206, 209, 216, 220, 223

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OFFSET

0,3

LINKS

Robin Visser, Table of n, a(n) for n = 0..10000

FORMULA

Probably a(n) ~ sqrt(2)*n*sqrt(log(n)) as n -> oo. - Robert Israel, May 02 2008

From Andrew V. Sutherland, May 02 2008: (Start)

This is supported by the following data:

n a(n) a(n)/n a(n)/(n*sqrt(log(n)))

------ ------ ------ ---------------------

2 4 2.0000 2.4022

4 10 2.5000 2.1233

8 24 3.0000 2.0804

16 53 3.3125 1.9894

32 115 3.5938 1.9304

64 244 3.8125 1.8695

128 514 4.0156 1.8230

256 1075 4.1992 1.7832

512 2237 4.3691 1.7493

1024 4642 4.5332 1.7218

2048 9608 4.6914 1.6990

4096 19843 4.8445 1.6797

8192 40895 4.9921 1.6630

16384 84129 5.1348 1.6483

32768 172797 5.2733 1.6354

65536 354437 5.4083 1.6240

131072 726143 5.5400 1.6139

(End)

MATHEMATICA

a = {1}; Do[AppendTo[a, Sum[Ceiling[n/a[[k]]], {k, 1, n}]], {n, 1, 70}]; a (* Stefan Steinerberger, Apr 04 2008 *)

CROSSREFS

Cf. A138812.

Sequence in context: A198266 A067497 A123384 * A310689 A184625 A184118

Adjacent sequences: A138810 A138811 A138812 * A138814 A138815 A138816

KEYWORD

nonn

AUTHOR

Leroy Quet, Mar 31 2008

EXTENSIONS

More terms from Stefan Steinerberger, Apr 04 2008

STATUS

approved